Rossouw blazed 121 off 51 balls with 12 fours and six sixes as Multan motored to a winning 6-244 with five balls to spare and book a playoffs spot on Friday.
Half-centuries by captain Babar Azam (73) and Saim Ayub (58) gave Peshawar an imposing total of 6-242.
But Rossouw, who also played for Sydney Thunder in the BBL, smashed his own record for fastest century in the PSL to give Multan their fifth win.
"When you're chasing such a high score, you have to go from ball one. Lucky for me, it's paid off tonight," Rossouw said. "This might be (my best Twenty20 innings ever) because it's a run chase and that's extra pressure, and everything adds up."
After adding a brisk 99 runs with Kieron Pollard (52), Rossouw raised his century off 41 balls and bettered his previous PSL record of a 43-ball century against Quetta in 2020.
Rossouw was eventually caught at long on by stand-in Peshawar captain Tom Kohler-Cadmore after Babar Azam felt sick at the change of innings.
Earlier, Babar and Saim shared a second successive century stand for Peshawar.
Multan fast bowler Abbas Afridi took 4-39 and Pollard made two brilliant catches on the boundary. But Kohler-Cadmore took 24 off the last over to leave fast bowler Anwar Ali with the second most expensive figures in the history of PSL - 1-66.
Multan joined Lahore Qalandars and Islamabad in the playoffs. Peshawar and Quetta Gladiators still have a chance to qualify.
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