The 35-year-old former Marseille striker was hugely impressive in a thrilling game, and his reward came from the spot in the 54th minute, with Mexican giants Tigres full value for their victory.
It means the CONCACAF Champions League winners will face face Al Ahly or Bayern Munich in the final on Thursday.
Tigres were overwhelmingly the dominant side in the first half at Education City Stadium in Al Rayyan, with Copa Libertadores winners Palmeiras kept in the game thanks to three terrific saves from goalkeeper Weverton.
The Brazil international denied Carlos Gonzalez inside the first five minutes by repelling the Paraguayan striker's meaty header.
Weverton then denied Gignac twice in four minutes, first pushing the ball wide for a corner in the 34th minute when the Frenchman looked to bend a shot inside the far right post from a tight angle. A better stop followed as the eye-catching Gignac had a fine header clawed away from the bottom right corner.
Gonzalez had his shirt tugged by Luan for the decisive penalty incident, with Gignac driving his kick into the bottom left corner.
Palmeiras pushed for an equaliser but had at least five men offside from a free-kick before putting the ball in the net, and then Tigres' Luis Rodriguez almost scored in the wrong goal from a low cross, the ball trickling six inches wide. Matias Vina had a shot deflect narrowly wide deep into stoppage time before Weverton, sent up for a corner, headed over from the last big chance.
Qatar Stars League champions Al Duhail earlier secured fifth place by beating K League 1 side Ulsan Hyundai 3-1 in their play-off.
At the Ahmad Bin Ali Stadium, Edmilson Junior gave Al Duhail a 21st-minute lead when he drove through midfield and swept a 25-yard shot into the bottom right corner, only for Yoon Bit-garam to level in the 62nd minute.
Mohammed Muntari restored Al Duhail's lead four minutes later with a volley from Dudu's sublime assist, a scooped ball over the defence, and Almoez Ali cracked in the third eight minutes from the end.