Defences were well on top in the St David’s Day Welsh derby at The Vetch Field with all the action confined to the closing minutes.
Wrexham had shouts for a penalty turned away as Andy Morrell was brought down in the penalty area.
However, as the visiting players continued to protest Swansea sent the ball upfield and substitute James Thomas fired a right-foot shot past veteran keeper Andy Dibble.
The ball struck the foot of the post and rebounded in to play where it was hacked clear by the Wrexham defence.
A draw was a fair result as neither side could stamp their authority on the game which only saw three shots on target.
"I prefer it to losing but both sides really wanted the three points today," said Wrexham boss Denis Smith after the match.
"It was a good game and Swansea defended very well. They will be safe if they can continue playing like that.
“I knew it would be a tight game even though we won 4-0 when we played them at our place earlier in the season because Brian Flynn has brought in some good players.
“We didn't create a great deal and probably a draw was a fair result." Flynn was given a problem in the days leading up to the match when he had to find a replacement keeper after Roger Freestone suffered back trouble in their last match at Hartlepool.
He eventually signed Neil Cutler from Nationwide Division One side Stoke City and he became the 21st player to make his debut for the Swans this season equalling a record set 18 years ago.
Cutler played for the Potters in last seasons Division Two play-off final against Brentford at the Millennium Stadium but has failed to hold down a regular spot with Stoke since the arrival of Tony Pulis.
"I'm delighted with a clean sheet and I am very happy with the defence as they made life very easy for me,†Cutler said.
“I didn’t know I was going out on loan until Friday afternoon and have had very little chance to meet the other players. The only way I’ve found of getting to know them was spotting their names on the back of their shirts during the game.â€