Du Plessis and Virat Kohli, who made 59, put together an opening stand of 137 to lay the foundations of Bangalore's 174-4 after being sent in to bat in the opening match of the day at Mohali.
Siraj then returned impressive figures of 4-21 and forced a run out to dismiss Punjab for 150 in 18.2 overs for Bangalore's third victory in six matches.
Kohli stood in as captain for du Plessis, who made the team as a batsman due to a rib injury he picked in the previous match and was later substituted under the new impact player rule.
The South African had lived up to the designation with a 56-ball knock laced with five sixes. He tops the tournament's batting chart with 343 runs, including four half-centuries.
Kohli has a total of 279 runs but Thursday's knock lacked his usual aggression.
Harpreet Brar broke the marathon stand to have Kohli caught behind and then snared Glenn Maxwell, who attempted to hit out on his first ball but was caught for a duck.
Du Plessis departed in the next over and the Punjab bowlers came back well to keep down Bangalore's score despite a solid foundation that had raised hopes of a 200-plus total.
Punjab lost wickets regularly in their reply and only Prabhsimran Singh, with a valiant 46 off 30 deliveries, and Jitesh Sharma's late blitz of 41 represented any real fight.
Siraj got two breakthroughs at the start, including the dangerous England import Liam Livingstone for two, and leg-spinner Wanindu Hasaranga bowled Australia's Matthew Short for eight.
Sam Curran, leading the Kings for the second straight game in the absence of injured skipper Shikhar Dhawan, was run out for 10.
Siraj came back to rattle the stumps twice and become the leading bowler in the tournament with 12 wickets.
