Boston United salvaged a vital point with a late goal from Adam Boyd.
It was a result that followed a week of turmoil at the club, after a takeover that had seen manager Neil Thompson depart in advance of the expected return of Steve Evans when his FA ban ends in two weeks time.
The game did not spark into life until the ninth minute when a raking 25-yard free-kick from Neil Redfearn flashed inches wide of the Swansea goal.
At the other end, home keeper Paul Bastock twice dropped easy catches and had to be rescued by his defenders.
But there was nothing he could do to prevent Leon Britton from slotting in from 15 yards following Brad Maylett's right-wing cross on 14 minutes.
Boston almost hit back moments later but Tom Bennett's effort was deflected over.
City went close again in the 15th minute from a pass inside by Lee Trundle and ten minutes later a sweetly struck 18-yard drive by Andy Robinson was pushed away for a corner by a diving Bastock.
Boston had a few forays in reply, notably down the flanks through Mark Angel and Lee Thompson, but the Swansea defence stayed resolute.
Just before the break the visitors almost scored again, but efforts from Lee Trundle and Leon Hylton were blocked.
Swansea resumed on the attack after the break and Bastock had to make two good saves to thwart Trundle and Roberto Martinez and then Maylett broke clear, but fired across goal.
United struggled to create any moments of danger although a long-range lob from Bennett had Roger Freestone panicking before dropping over the top.
Boston lost the services through injury of their main midfield influence, Readfearn, on the hour and found it increasingly difficult to put any cohesive moves together.
That was until the 72nd minute when neat play down the left led to a shooting chance for substitute Peter Duffield, but Freestone saved well.
Swansea's swift counter attacking play brought a 75th minute chance for Robinson, but his low drive flashed wide.
Boston tried to summon a late rally and twice Duffield went close with headers from Bennett crosses, the second of which was tipped onto the bar by Freestone.
Boston's efforts though, yielded reward on 87 minutes when Stuart Douglas headed Thompson's cross from the right back across goal and Boyd pounced to fire in from eight yards.