Two second half goals sealed defeat for Dover in a hard fought contest at Huish Park.
Whites were ahead inside 15 minutes through Ade Azeez, before Joe Quigley levelled just before the break.
Quigley then doubled his tally early in the second half before Rhys Murphy sealed it with just over 10 minutes to play.
Both sides had early chances with Quigley heading over for the hosts after connecting to a Josh Neufville cross.
Shortly after, Oscar Gobern nearly gave Whites the lead after a deep free kick from Sam Wood was headed back across goal to the midfielder, but his shot was cleared for a corner.
From the corner, Whites did take the lead through Azeez after he was able to poke the ball past home goalkeeper Adam Smith after the stopper had palmed a shot straight out to the Dover striker.
Travis Gregory almost doubled Whites’ advantage on the stroke of half time, but his looping shot from outside the area just missed the target.
Whites were made to rue this miss as Yeovil went straight down the other end to level through Quigley who fired home the equaliser.
Quigley doubled his tally and completed Yeovil’s turnaround minutes into the second half as Alex Bradley’s cross found the forward who headed it over Ollie Webber in the Dover goal.
Murphy doubled Yeovil’s lead with his first touch after coming off the bench, connecting to a free kick crossed towards the back post to seal victory for The Glovers.
Quigley almost sealed his hat trick late on from the penalty spot, but Webber, who had given the penalty away, made up for his mistake by making a great save to deny the Yeovil striker.
Earlier in the day, Andy Hessenthaler named an unchanged lineup from Tuesday’s win against Barnet.
Dover’s suffered FA Cup heartbreak after losing on penalties at a wet Huish Park on Saturday.
With both sides successfully converting a total of 13 times from 12 yards, Marshall Wratten saw his spot kick saved by home keeper Adam Smith in sudden death.
Andy Hessenthaler’s side had twice fought back to level the scores during an end-to-end affair. Rhys Murphy scored an early brace, but Louis Collins’ quick-fire double had Whites back on terms at the break.
Joe Quigley headed the Glovers back ahead just after the restart, however TJ Bramble prodded in Whites’ third of the match shortly after the hour mark to take the game to penalties.
The shootout defeat saw Dover fail to reach the first round proper of the FA Cup for the first time in three seasons, though it looked like their exit from this season’s competition was to be confirmed much earlier thanks to Murphy’s early double.
The striker rifled a left-footed shot into the bottom corner and soon after Josh Staunton had headed against the post, Murphy grabbed another, stabbing in a corner from close range to leave Whites staring at a fifth consecutive loss.
The visitors rallied, with Josh Passley’s rampaging run and pass finding Collins to finish neatly at the far post.
Hessenthaler’s men then struck again with half-time looming as Collins grabbed his second of the match, poaching on Marvel Ekpiteta’s looping header across the goalmouth.
There was still time for Tom Smith, making his debut for Dover following a loan move from Premier League side Arsenal last week, to turn Gabriel Rogers shot around the post.
Smith was at it again after the restart by saving Quigley’s strike, but Dover’s stopper was powerless to stop the burly striker heading in Dan Leadbitter’s cross.
Yeovil continued to attack and Lawson D’Ath was left frustrated as Smith tipped his goalbound shot away for a corner.
Smith’s namesake at the other end was then called into action, blocking from Collins at the far post.
Collins then turned creator for Bramble, heading across the box for the midfielder to slide in Whites’ latest leveller.
Tom Smith acrobatically saved Staunton’s header and Kurtis Cumberbatch nearly completed a remarkable comeback for Whites, sending a free header straight at Adam Smith.
Rogers almost won it from the glovers, only to be denied by Smith once again.
But it was Adam rather than Tom who stole the headlines in the shootout, saving the crucial penalty to send the Somerset side through to the next round of the cup.
Earlier, Hessenthaler made five changes to the side that started the 2-0 defeat at Torquay last week. Bilel Hinchiri, Collins, Wratten and Smith replaced Ade Azeez, Steven Rigg, Yusuf Mersin and Sam Wood who were named as substitutes. Ekpiteta also returned in place of the injured Will De Havilland.
Whites next host Eastleigh in the National League on Tuesday 27th October, kick off 7:45 pm.
Scott Doe’s second half goal handed Athletic all three points in front of the TV cameras on Saturday evening.
Man-of-the-match Doe coolly finished Jack Munns’ free kick on the hour mark as Andy Hessenthaler’s men extended their unbeaten run to four matches.
And at the other end Dover’s experienced centre-back superbly marshalled his defence to a third consecutive clean sheet.
Earlier, Yusuf Mersin was called into action early on, pawing out Lawson D’Ath’s goalbound volley with the Dover defence on hand to clear the ball for their goalkeeper.
Whites were then denied by the woodwork on 10 minutes.
Paul Rooney’s volley from Doe’s knock-down deflected into the air, with Steven Rigg nodding onto the bar from a few yards out.
Inih Effiong then connected with Aaron Simpson’s cross, heading straight at home keeper Stuart Nelson.
Dover were then required to clear off the line once again when Rhys Murphy nodded over Mersin, however Rooney strode across the goalmouth and blasted the ball away for a throw-in.
Myles Hippolyte had Mersin scrambling back towards his goal, however the Yeovil man’s header bounced onto the roof of the net.
Murphy continued to search for his 10th goal of the season, racing onto a long ball and volleying just off target.
Town then went closer with the half-time whistle just five minutes away.
Tom Bradbury connected with D’Ath’s curling corner, only to head wide of Mersin’s far post.
Bobby-Joe Taylor fired over Nelson’s goal from distance and following the restart, Murphy turned inside Doe and fired towards goal, a stinging effort that Mersin had to pat down.
Nelson then clutched onto Rigg’s header from Munns’ corner and Yeovil’s stopper had to turn Effiong’s angled drive around the post.
But Dover did go ahead two minutes after the hour mark thanks to Scott Doe’s first goal of the season.
The defender found himself unmarked in the box and after collecting Munns’ set piece, poked the ball past the onrushing Nelson.
Nelson then had to come to the hosts’ rescue again when Effiong sprinted clear off the home defence, saving the striker’s shot with his legs.
Mersin palmed Gold Omotayo’s fierce volley into the side netting as Dover continued to repel the home team’s attacks.
Mersin saved his best saves for the 80 minute mark, beating away sub James Tilley’s 20-yard drive and then getting fingertips to Hippolyte’s curling effort.
Sub Roberto Ratti was then inches from sealing the win with three minutes to go, smacking the bar with a diving header.
But Athletic’s resilient defence held on to their lead until the final whistle, with Doe receiving a £200 cheque for the charity of his choice from BT Sport for his man-of-the-match performance.
The win sees Dover move up two places to 10th on the National League table, two points of seventh-place Harrogate Town.
Earlier, Hessenthaler made one change to the side that started against Southend United in the FA Cup, with Nassim L’Ghoul replacing the suspended Jai Reason.
Whites next host Solihull Moors on Saturday 23rd November, kick off 3 pm.
DOVER ATHLETIC REACTION