The 22-year-old stand-in captain struck 63 not out off 38 deliveries as Perth recovered from 62-7 to chase down 125 and end Lahore's chances of making the last four.
Marsh rounded off proceedings in spectacular fashion, striking Wahab Riaz (0-29 from three overs) back over his head for successive sixes to complete victory with an over to spare.
The Scorchers had already been eliminated and their success against Lahore ensures the Chennai Super Kings join the Kolkata Knight Riders in qualifying from Group A.
Having been put into bat, the Lions knew they needed to prevail by 46 runs to claim a semi-final berth.
They started badly, though, losing Nasir Jamshed (one) and Umar Siddiq (one) in the first over from Joel Paris (3-22 from four).
When skipper Mohammad Hafeez and Wahab followed to Marsh (2-12 from three) for ducks, Lahore were in disarray at 11-4.
However, Saad Nasim did his best to inspire a recovery, striking an unbeaten 69 from 55 balls with the aid of seven fours and a six.
Umar Akmal (26) and Mohammad Saeed (20) offered valuable support as Lahore scrambled to 124-6.
Perth were then reduced to 27-4 in reply, providing hope for Hafeez's men as they aimed to dismiss their oppponents for 78 or less.
Hafeez returned exceptional figures of 2-8 from four overs and the Scorchers were still in deep trouble at 62-7 when Yasir Arafat (three) was run out at the start of the 13th over.
However, that brought Marsh and Brad Hogg and they bludgeoned runs all around the ground in a superb display of defiance.
Marsh's 63 included seven fours and three huge maximums, while his veteran partner cleared the ropes twice on his way to 28 not out from 19 deliveries.
Perth still required 16 for victory with two overs remaining, but then took 21 from Wahab to bring the game to a swift close.