Pablo Counago's first goal of the season gave Town a point after Blues had fallen behind early again.
Craig Beattie gave Swansea the advantage on seven minutes when in-decision in the home defence presented the striker with a chance that he buried from 15 yards.
Blues were level though before the quarter hour with Counago, who turned down a move to Swansea before the season kicked off, scoring from close range after good link up play with Jaime Peters.
Connor Wickham had the clearest chance to win the game for Town deep into the second-half but Dorus De Vries blocked his effort and Liam Trotter blasted over in added on time.
Roy Keane made three changes to the side that went down at Barnsley before the international break, Asmir Begovic coming in for his debut after joining on loan from Portsmouth in midweek. David Wright returned to the side at left-back with Counago starting upfront. Richard Wright, Carlos Edwards and Tamas Priskin making way.
Swansea started the better side and Gareth McAuley was at full stretch to clear from Mark Gower's cross, Liam Rosenior then doing well to get a block on Andrea Orlandi.
Dorus De Vries punched clear from Jon Walters from Alan Quinn's cross before the Welsh club went ahead, Beattie latching onto a long ball that evaded Tommy Smith and beating Begovic from a tight angle.
The Scotland international was close to grabbing a second soon after but he didn't get enough on Gower's cross to beat Begovic.
Smith had a header cleared from a Grant Leadbitter corner as Town rallied and Blues were level on 14 minutes, Counago and Jaime Peters exchanging passes with the Spaniard sliding the ball calmly into the net from eight yards.
McAuley's header almost set up Counago, the striker then close to finding Walters before Alan Tate's interception.
Counago robbed Ashley Williams inside the Swans' box but couldn't make it pay while at the other end, McAuley won his battle with Beattie to clear from Gower's cross. Counago headed over from Peters' cross as the first-half came to an end.
The two carried on where they left off immediately after the break, Peters this time sending a left foot effort over the bar.
De Vries saved well from Leadbitter's low shot after a driving run by Peters, Walters' head on met with a left foot effort from Counago that forced De Vries into another save.
Walters was inches away from putting Town ahead on the hour, Quinn's cross sidefooted wide at the nearpost before Quinn made way for Wickham, Jordi Lopez also joining the action for Orlandi.
Nathan Dyer stabbed the ball wide at the far post, Beattie then seeing a volley blocked as Town struggled to clear.
Peters made way for Lee Martin for the closing 20 minutes, Tom Butler on for Dyer as both sides made a second change. Angel Rangel getting the first booking of the game soon after for a foul on Martin.
Leadbitter had a header from 18 yards saved by De Vries after Wickham had launched a long throw into the box while at the other end Williams headed over from Lopez's cross.
Wickham had a gilt edged chance to put Town ahead seven minutes from time but De Vries made the block with his outstretched left foot.
Fourth official Mr Hambling took over from referee Keith Wright for the last exchanges with one last chance falling to Trotter who shot over, leaving Town still searching for that first win.
Town: Begovic, Rosenior, McAuley, Smith, D.Wright, Peters (Martin 72), Leadbitter, Trotter (Colback 90), Quinn (Wickham 61), Walters, Counago. Subs not used: Lee-Barrett, Bruce, Balkestein, Priskin.
Swansea: De Vries, Rangel, Williams, Tate, Bessone, Britton, Pratley, Orlandi (Lopez 62), Gower (Richards 90), Dyer, Beattie. Subs not used: Cornell, Van der Gun, Trundle, Butler, Idrizaj. Booked: Rangel.
Att: 19,667




















