Goals from Scott Sinclair, Darren Pratley and Joe Allen mean Brendan Rodgers' side are four points outside the automatic promotion places in third, and six behind their Welsh rivals who moved to the summit with victory over Norwich.
By contrast Palace have won just once in their last seven league games and their worst start to a season for a decade has seen them slip to the bottom of the Championship.
Influential midfielder Darren Ambrose returned to the Palace squad for the first time since picking up a foot injury in August and was named among the substitutes.
Eagles boss George Burley made three changes to the side that lost 4-3 to Preston last weekend - David Wright, Adam Barrett and former Holland international Edgar Davids coming in for Anthony Gardener, Alex Marrow and Julian Bennett.
Ashley Williams, Dorus de Vries, Nathan Dyer, Orlandi, Allen and top scorer Sinclair all returned to the Swansea side after being rested for the 2-0 Carling Cup defeat at Wigan in midweek.
And on his return to the ground when he spent time on loan in 2008, Sinclair opened the scoring in the sixth minute with his 11th of the season.
Davids handled a cross from Angel Rangel and the referee's assistant flagged for a penalty, but advantage was played and Sinclair poked home from close range.
Sinclair's strike partner Marvin Emnes had an effort blocked in the area shortly after, while Palace had their first effort on goal in the 15th minute when Adam Barrett's dipping 30 yard drive went narrowly over.
Swansea's early dominance gave way as Palace felt their way back into the game and Kieran Djilali fired wide after exchanging passes with David Wright.
Palace lost Owen Garvan through injury moments before James Vaughan gave De Vries his first meaningful action in the 34th minute with a well-hit free-kick that the Swans goalkeeper stretched to hold.
The home side finished the half strongly but Lionel Speroni had to react smartly to stop a Nathan Dyer drive after a menacing run from the Swansea winger.
Djilali sliced wide from 12 yards seven minutes after half-time following a one-two with Vaughan and he was replaced by Ambrose on the hour.
Speroni made a stunning save with 20 minutes remaining, tipping a rasping effort from Dyer over the bar.
From the resulting corner Swansea doubled their lead, as Alan Tate flicked on Orlandi's delivery to leave Pratley with a simple finish.
The points were secured 10 minutes from time when Allen found Pratley and continued his run to collect the cut back and roll the ball past Speroni.
An influential second-half performance from Pratley was soured when he collected a booking for a foul on Wright with eight minutes remaining which will rule him out of the Cardiff clash.