A second-half penalty from Lee Trundle earned the Swans a share of the spoils at the Liberty Stadium after Marcus Stewart had given the Glovers the lead.
Swansea City: Gueret, Amankwaah, Austin, Tate, Iriekpen, Britton, Pratley (capt), Robinson, Williams, Trundle, Fallon. Subs: Oakes, Akinfenwa, Butler, Way, O'Leary.
Yeovil Town: Mildenhall, Jones, Skiverton (capt), Forbes, Terry, Gray, Cohen, Kalala, Lynch, Morris, Stewart. Subs: Guyett, Barry, Webb, Welsh, James.
Ref: P W Melin
Asst-refs: P N Gibbs, A D Sainsbury
4th official: G D Scott
Att: 14,513
Swans boss Kenny Jackett was given a pre-match boost with Lee Trundle, Andy Robinson and Leon Britton all passing fitness tests.
With Leon Knight suspended, Trundle returned to partner Rory Fallon up front.
At the back, Kevin Amankwaah started at right-back against his former side, while Kevin Austin was on the left. In the heart of defence, Izzy Irekpen and Alan Tate made up the same back four that kept a clean sheet in the 1-0 win at Leyton Orient last Saturday.
Britton started on the right of midfield with Tom Williams on the left. Robinson moved into the middle with skipper Darren Pratley.
There was also a welcome return for midfielder Darren Way who started on the bench against his former club. It was his first appearance at the Liberty since March after a shin injury.
Yeovil arrived full of confidence after their 1-0 win over high-flying Port Vale.
Manager Russell Slade included new signings Marcus Stewart and Mark Lynch as the Glovers returned to the Liberty Stadium for their second Friday night fixture in consecutive seasons.
After an even opening, Yeovil posed the first threat when a dangerous cross from Chris Cohen after six minutes edged towards Wayne Gray at the far post. But Willy Gueret smothered the danger with the help of Austin.
Swansea responded via Robinson who was brought down on the edge of the area. Robinson picked himself up to curl the free kick towards the top corner, only for Steve Mildenhall to pull off a great save.
There seemed more fluidity to Swansea's game than their last home performance against Doncaster as a sweeping move in the 13th minute created the first chance for Fallon. Amankwaah, who was being booed by the Yeovil fans, drove forward before finding Britton. The midfielder delivered a great cross which Fallon met well, only to see his header fly just wide.
Amankwaah was back carrying out his defensive duties in the 18th minute as he deflected a Lee Morris shot into the side netting.
Swansea were enjoying the better possession, however, as Paul Terry, brother of England international John, picked up the first yellow card of the game in the 24th minute for a foul on the lively Pratley.
He was joined a minute later by Tom Williams for the Swans.
The Swans were well in control at the half hour mark without really troubling Mildenhall in the Yeovil goal, as their approach play in the final third let them down.
When Yeovil did apply any pressure at the other end, the Swans back four looked solid.
It made for a goalless first half.
Half-time: Swans 0 Yeovil 0
Adebayo Akinfenwa replaced Fallon up front for the start of the second-half.
The Swans were soon chasing the game, however, after Marcus Stewart gave Yeovil a 53rd minute lead.
New signing Stewart thought he had missed his chance when Tate cleared his 49th minute lob over Gueret off the line.
But four minutes later and he was celebrating his first goal for the Glovers when he stooped to head a Lee Morris corner beyond Gueret.
Two minutes later and it could have been 2-0 as the unmarked Chris Cohen shot straight at Gueret from eight yards out.
Jackett responded in the 59th minute by bringing on Darren Way for Williams. Way moved into the centre and Robinson went left.
The equaliser nearly came in the 61st minute as the crowd tried to lift the home team. Good work from Britton down the right saw his cross fall to Robinson whose snap shot struck the bar.
A minute later though and Swansea had their chance as battling Akinfenwa was pulled down inside the area by Terrell Forbes. Referee Paul Melin pointed to the spot, booked Forbes and Lee Trundle stepped up to smash the ball straight down the middle past Mildenhall.
It was Swansea's first success from the spot in three attempts after previous misses from Trundle and Leon Knight.
Akinfenwa was having a massive impact as he battled his way through the Yeovil defence, setting up a chance for Robinson who felt he was fouled just outside the area.
It was all Swansea approaching the last 10 minutes as Yeovil made a double substitution bringing on Welsh and Barry for Morris and Kalala, while Jackett played his final card by replacing Britton with Tom Butler.
With three minutes remaining, good work from Butler earned Swansea a corner, but there was still no way through as Tate tried his luck from long range.
As the fourth official indicated four minutes of injury time, Trundle weaved his way passed four challenges and into the area only to shoot inches wide.
