It looked like Gylfi Sigurdsson's goal would continue Swansea's revival under Francesco Guidolin with a third straight win and see the Welsh side go above West Brom in the Barclays Premier League table.
But Lukasz Fabianski, who had been in decent form on the night, was finally beaten in the second minute of time added on when Rondon blasted the ball home from close range after a scramble inside the six-yard box, and it finished 1-1.
It was harsh on Fabianski, who had produced good saves to deny Darren Fletcher and Stephane Sessegnon, most notably.
West Brom turned down bids for Saido Berahino on Monday because they felt his goals could keep them up, so - after watching his team struggle and miss chances - boss Tony Pulis will be hoping his striker will be fit enough to start soon.
Berahino, the subject of a £20million-plus bid from Newcastle on transfer deadline day, began on the bench because of a dead leg.
He must have wished he was on the field as he watched Fletcher squander three decent opportunities.
The first was after just two minutes when a Craig Dawson cross found Fletcher and his header was tipped over the crossbar by Fabianski.
Fletcher soon had another chance but tried to head James McClean's cross back across the six-yard box for Rondon rather than go for goal himself.
After half an hour there was some great improvisation from Sigurdsson, who seized on a loose ball 30 yards out and hit a dipping volley that had Ben Foster scrambling back towards his line, but the West Brom goalkeeper managed to push the ball round the post.
Dawson glanced a header wide from 10 yards out, while at the other end substitute Alberto Paloschi came on for his Swansea debut and the £8million signing from Chievo almost made an immediate impact.
Paloschi latched on to Wayne Routledge's through ball but Foster was quick off his line to block the Italian's shot.
Fabianski finished the half as he began it, acrobatically tipping an effort over the crossbar - this time keeping out Sessegnon's free-kick.
Fletcher fluffed a third headed opportunity early in the second half from a McClean cross
It was the kind of chance Berahino would bury and in the 62nd minute - after five minutes of songs about him from the home fans - he was introduced from the bench.
But two minutes later the hosts were behind
Paloschi could not keep hold of Leon Britton's pass and the ball broke to Sigurdsson down the right side of the penalty box and he steered a shot across Foster and into the bottom corner of the net.
Berahino serenades turned into chants of ''You don't know what you're doing'' as the Albion fans realised their team was up against it.
Pulis responded by putting on Victor Anichebe and he saw a well-struck shot brush Fabianski's fingertips as the ball flew narrowly past the top corner.
Paloschi poked the ball against a post in the 88th minute before Rondon had the final say.
Source : PA
Source: PA