The Swans, who made sure of their Premier League status for another season last weekend, fell behind to a Jonny Evans goal in the first half but successfully recovered in the final 20 minutes.
Another big opening came and went for Rondon as he failed to get the better of Nordfeldt when getting in behind the Swans' defence, although the visitors did not have to wait too much longer for their breakthrough.
Evans nodded home from a corner to score just Albion's seventh goal in their last 12 outings, of which they have now won only one due to City's impressive fightback.
Only an impressive challenge from skipper Leon Britton early in the second half denied Rondon a strike on goal, but Swansea created an opportunity of their own which Federico Fernandez failed to take by heading wide from a good position.
Swansea were on level terms with a quarter of the match left to play, though, thanks to Ayew's first goal for the club from a close-range header.
Ayew came close to a second when rifling into the side-netting, but the home side did find a winner through star striker Llorente, who belted home from Luciano Narsingh's accurate delivery.