Palace have endured a turbulent start to the season following the sudden departure of manager Tony Pulis, which was followed by defeats against London rivals Arsenal and West Ham in the Premier League.
The Selhurst Park outfit have been frustrated in their search for a successor to Pulis, but their supporters were finally given a reason to be cheerful as Gayle staked a major claim for a starting berth at Newcastle United on Saturday.
Making his first start of the season, the striker stunned League One Walsall by scoring all three goals in the first half in a one-sided tie at the Bescot Stadium as Palace eased into the third round.
Walsall had no answer to the impressive Gayle, who was a constant menace to the home defence and although Ashley Grimes was denied by the post in the second half it was a comfortable win for the visitors.
Palace caretaker manager Keith Millen rued his side's "flat and lacklustre" display against West Ham on Saturday and responded by making nine changes to his starting line-up.
Only Damien Delaney and Barry Bannan retained their places, while winger Anthony Forde made his home debut for a Walsall side that have failed to win in the third tier so far this season.
Palace soon stamped their authority on the game and they were in front just six minutes in courtesy of a clinical finish from Gayle.
Adlene Guedioura picked out the former Peterborough United man with a quick free-kick and Gayle showed a sharp turn of pace to race clear and shoot powerfully beyond Walsall keeper Richard O'Donnell from a tight angle.
The lively Gayle could have had a second goal soon after his opener, but just failed to get on the end of Jerome Thomas' dangerous cross.
Gayle was on target again 25 minutes in, though, firing a free-kick through the wall from just outside the penalty area after Glenn Murray had been upended by Adam Chambers.
Walsall were unable to live with the Palace frontman, who looked like he had a point to prove, and he completed his hat-trick four minutes before the break.
This time Gayle picked up a ball from Thomas and surged forward before finding the back of the net once again with an emphatic finish.
Walsall almost had a lifeline five minutes after the break, when Grimes' header came back off the post and hit Wayne Hennessey before Palace cleared.
Murray tried to get in on the act, but the Palace striker's long-range effort flashed just wide of O'Donnell's left-hand post.
Gayle was replaced by teenager Jake Gray just after the hour-mark with the game long since finished as a contest.
