Struggling Rotherham claimed an unlikely lead but Lee Trundle pounced to level before half time and Marcus Bean produced a second-half strike to edge the visitors ahead.
In the opening minutes Adebayo Akinfenwa's clever link with Bean opened up the home defence but his shot was blocked.
And another crucial block shut out Leon Britton after Kevin McLeod played it through as Swansea turned on the pressure.
Trundle might have won a penalty after 10 minutes when he used his strength and guile to wrong foot Colin Murdock.
But Irish international Murdock used his experience and produced a clever tug which was enough to pull Trundle off balance but not enough to persuade referee Mike Pike to give him a penalty.
A flick-on triggered Trundle again after 21 minutes but his shot on the turn was high and wide.
McLeod found space on the right and moved inside but could only produce another wayward effort.
The Welshmen were rocked four minutes from half time when Rotherham went in front with their first serious effort.
Midfielder Michael Keane produced a super ball through for Grant Leadbitter and the on-loan Sunderland man raced through to slot a cool shot pas the advancing Willie Gueret.
But the visitors were back level within 60 seconds with their first effort on target. Straight from the restart Swansea bounced back as Britton slid a neat ball for Trundle who turned cleverly and crashed a left-foot shot past Gary Montgomery.
Ten minutes into the second half Swansea might have been in front when Gueret launched a monster goal kick that had the home side back pedaling but Montgomery managed to claw the ball away from Trundle.
Four minutes later Bean gave Swansea the lead when he drilled in a low shot following assists from Trundle and Akinfenwa.
Gueret needed to produce a stunning save to deny Rotherham when Andy Monkhouse threaded a ball through for Martin Butler who saw his sharp shot saved one handed.
But in injury time Rotherham claimed a point when Deon Burton showed skill and poise before setting up Conlon who finished with a fierce shot.