They had fallen behind to a Eugen Bopp strike early in the second half but deserved to at least share the spoils after dominating the game for long periods.
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In goal for the Millers was Neil Cutler, who played on-loan for the Swans in 2003.
It was Butler who had the first strike on goal in the third minute but Cutler was well positioned to gather cleanly.
Marcos Painter was yellow carded after a lunge on Justin Cochrane that left the visiting midfielder needing attention.
The Swans went back on attack and a Lee Trundle free-kick rebounded off the wall to Rory Fallon who tried a chip shot which Cutler brilliantly tipped over.
Rotherham's first goal attempt came in the 25th minute when a neat turn by Martin Woods set him in the clear but Willie Gueret came out to block his shot.
Back came the Swans and a Trundle corner caused problems for the defence but Dennis Lawrence lifted a loose ball high over the crossbar.
Just before the interval Leon Britton missed a glorious chance to break the deadlock when he scooped over from inside the six-yard box as the defenders went looking for an offside flag.
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The goal stung the Swans into action and Lawrence had a header from a Trundle free-kick kicked over by the alert Cutler before Fallon headed wide when well placed.
The mis-firing Fallon then headed another opportunity high and wide from an Ian Craney corner.
Akinfenwa replaced Painter with ten minutes remaining as Swans boss Kenny Jackett tried to rescue something from the game they should have won comfortably.
One minute from normal time Akinfenwa saved Swansea with a glancing header from an Alan Tate cross to deservedly level the score.