Chasing a target of 207, North romped home with Yuvraj remaining unbeaten on 100 (16 x 4) on the penultimate day of the rubber at the K D Singh Babu Stadium.
Yuvraj, declared the Man of the Match, added 170 for the second wicket with Gautam Gambhir, who was equally impressive in scoring an unbeaten 79.
The stylish Punjab left-hander, who came at the fall of Virender Sehwag (15), exhibited an array of attractive shots on either side of the wicket and raced to his hundred in 115 balls. Yuvraj was particularly severe on star pace bowler Zaheer Khan, carting him for four boundaries in his two successive overs.
Earlier, West, resuming at their overnight score of 146 for five, lost wickets in quick succession and were bundled out for 201 in 63.1 overs.
Leg-spinner Amit Mishra emerged as the most successful bowler, scalping five for 52 runs.
Barring opener Wasim Jaffer (47), Kiran Pawar (37) and all-rounder Rajesh Pawar (39), none of the other West batsmen impressed as the last six wickets managed to add only 81 runs.
North began their chase on a cautious note but soon lost Sehwag when he tried to loft a flighted delivery from Pawar. Sehwag, who made 33 in the first innings, was caught at long of by Zaheer Khan.
Gambhir, however, carried on carefully and slowly came up with some fine shots to make 79 with the help of nine boundaries.
But the crowd puller was undoubtedly Yuvraj as he delighted the spectators with his power play, negotiating both pacers and spinners with amazing ease.