Rangers have now gone eight matches without a win and Warburton's position as manager is under scrutiny.
There are no such problems for Swans boss Steve Cooper, whose side moved up to second in the Sky Bet Championship table.
Ayew put the visitors ahead in bizarre fashion a minute before half-time.
Jake Bidwell's header from Connor Roberts' right-wing cross appeared to be going wide but R's defender Yoann Barbet headed the ball against the woodwork, leaving goalkeeper Seny Dieng stranded – and Ayew with an open goal.
Both sides had created chances during what was a fairly even first half up to Ayew's opener.
Lowe was put through by Ayew's pass but shot straight at Dieng, who later saved a long-range effort from Yan Dhanda.
At the other end, Ilias Chair caused problems for Swansea on the right, serving up a cross which just evaded Macauley Bonne, who also headed over after being found by Barbet's diagonal ball from the left.
Conceding such a soft goal was a sickener for Rangers, who fell further behind after being caught on the counter-attack nine minutes into the second half.
Lowe raced onto Matt Grimes' ball forward and slotted past Dieng – his fourth goal is as many games and sixth of the season.
But Bonne failed to make an impact and missed another decent chance when he was unable to get a firm header to Rob Dickie's cross.
And while Dykes has been a revelation for Scotland, establishing himself as their number nine since his summer move from Livingston, he has scored only once from open play for QPR and was easily contained by Swansea's impressive defence.
Cooper's men were more than comfortable, although substitute Charlie Kelman did almost pull a goal back when he was just unable to make contact at the far post with Barbet's cross from the left.