Cameron Green (41) and Suryakumar Yadav (33) put on 66 to help guide five-time champions Mumbai to 182-8 after they elected to bat first in the knockout contest in Chennai.
Madhwal then returned figures of 5-5 in 3.3 overs to dismiss Lucknow for 101 as Mumbai booked a meeting with holders Gujarat Titans in the next play-off encounter on Friday.
The winners of that clash will meet Chennai Super Kings in the final in Ahmedabad on Sunday.
Lucknow's innings imploded as they collapsed from 69-2 to be bowled out in 16.3 overs, losing three key wickets to run outs.
Green, who hit his maiden T20 century in Mumbai's previous win, looked in control during his 23-ball knock until his departure.
Naveen-ul-Haq, who took four wickets for Lucknow, sent back Suryakumar and Green, bowled by a slower off-cutter from the Afghanistan pace bowler, in the space of three deliveries to push Mumbai onto the back foot.
Tilak Varma hit back with a quickfire 26 and a 43-run stand with Tim David, who was out caught for 13 after unsuccessfully reviewing a full toss for being over waist-height.
Naveen finished with 4-38 and Yash Thakur took three wickets but despite their efforts Mumbai's impact sub Nehal Wadhera boosted the total with his 12-ball 23.
Lucknow lost their openers early including impact player Kyle Mayers for 18 before Australia's Marcus Stoinis attempted to pull the chase together in his 27-ball 40.
But Madhwal struck with successive balls, including getting the dangerous Nicholas Pooran caught behind for a golden duck.
Stoinis, who crossed 400 runs this season to be his team's standout performer, was run out after a mid-pitch collision with non-striker Deepak Hooda with both batsmen watching the ball.
The innings fell further apart with two more run outs sending back Krishnappa Gowtham and Hooda.
Lucknow, who made their IPL debut last season with Gujarat as the league grew to 10 teams, fell at the same hurdle in the previous edition.
The neutral venue for both teams had many empty seats, in contrast to the nearly full stadium on Tuesday when home hero MS Dhoni's Chennai made the final with a win over Gujarat.
