Put in to bat, Mumbai scored 286 for eight in 50 overs, thanks to a 135-run fourth-wicket partnership between Shreyas Iyer (77) and Suryakumar Yadav (67).
In reply, Pandey anchored the chase with an unbeaten 99 off 112 balls, that had nine fours and a six, as Karnataka reached the target with couple of balls to spare.
Karnataka will meet Bengal in the semi-finals.
A couple of weeks earlier, Pandey scored a century for India ‘A’ against Sri Lanka in a practice game in Mumbai. On Friday he was involved in two important partnerships that helped Karnataka reach the target easily.
Along and India all-rounder Stuart Binny (58) he added 119 runs for the fourth wicket, while with Karun Nair (32 off 23 balls) he gathered 60 priceless runs to seal the deal.
Binny's 58 came, off 67 balls, included three fours and a six. His stand with Pandey steadied the Karnataka innings when they were in a spot of bother at 84 for three.
Earlier, skipper Surya and former India Under-19 Iyer came together at the fall of the third Mumbai wicket with scoreboard reading 59. The duo batted with a lot of composure adding 135 runs in 23.1 overs before Abhimanyu Mithun (2/57) cleaned up the Mumbai captain.
Both Iyer and Surya, who slammed four boundaries and three sixes, were especially severe on left-arm bowler Srinath Aravind (2/73), who bowled left-arm spin apart from his gentle medium pacers.
Iyer should have got to the three-figure mark but Pandey's gentle medium pacers did him in as he spooned a return catch.
Mumbai also suffered because veteran Wasim Jaffer (18) was out cheaply, caught by Pandey off Mithun.
When Karnataka batted, Mumbai were never in the match once Pandey joined forces with Binny.
Brief scores:
Mumbai: 286-8 (Shreyas Iyer 77, Suryakumar Yadav 67, Abhimanyu Mithun 2/57, Srinath Aravind 2/73).
Karnataka: 287-6 (Manish Pandey 99 not out, Stuart Binny 58, Saurabh Netravalkar 2/43). Karnataka win by 4 wickets.
Yuvraj, Gurkeerat help Punjab beat Railways
Half-centuries from Yuvraj Singh and Gurkeerat Singh Mann helped Punjab beat Railways by five and also make the semi-finals, in another match in Vadodara.
They will play Odisha for a berth in the final.
Chasing 243 at the Motibaug Cricket Ground, the Harbhajan Singh-led side rode a 75-run fourth-wicket partnership between Yuvraj (56) and Gurkeerat (56 not out) to achieve the target in 47.2 overs.
Sharing the new ball with Anureet Singh, medium-pacer Amit Mishra did pose a challenge to the Punjab chase by picking up three wickets but the top and the middle-order stood up to the test.
Still eyeing a 2015 World Cup berth, out-of-favour Indian southpaw Yuvraj struck five fours and four sixes in his 52-ball stay while Gurkeerat hit seven boundaries off 54 balls.
Amitoze Singh (43), Manan Vohra (32) and Mandeep Singh (32) also came up with useful contributions.
Earlier, put in to bat, Railways suffered from lack of partnerships but No. 3 batsman Anustup Majumdar ensured that the Mahesh Rawat-led side posted a respectable 242 for nine in 50 overs.
Punjab medium-pacer Baltej Singh was the wrecker-in-chief with a five-wicket haul. He and pace spearhead Sandeep Sharma hurt the Railways batting-order time and again.
Brief scores:
Railways: 242-9 in 50 overs (Anustup Majumdar 76, Asad Ullah Khan Pathan 31; Baltej Singh 5-33)
Punjab: 247-5 in 47.2 overs (Yuvraj SIngh 56, Gurkeerat Singh Mann 56 not out; Amit Mishra 3-42).
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