The 40-run win that gave India the "fancied" series 3-2 was built on a wristy 107 by VVS Laxman, followed up by another brilliant bowling display by left-arm seamer Irfan Pathan (3/32) who helped reduce the home side to 96 for six atone stage.
A fightback by wicketkeeper Moin Khan, who made 72, and Shoaib Malik, 65, was not enough for their team to overtake India's 293 for seven and the home side were all out for 253 in the 48th over.
Never before has India won a One-day, or for that matter a Test series, in Pakistan. It has lost all the five previous series of the game's shorter version in this country and its facile win before a packed Gaddafi stadium was a sweet triumph.
In contrast to the first four thrilling matches of the series which was tied 2-2, Wednesday's decider was in sharp contrast with India, having been put in, notching up 293 and then holding the upper hand throughout except when Moin and Malik put on a brave 99 runs for the seventh wicket.
Captain Inzamam-ul Haq, later declared Man of the Series, and Younis Khan tried to salvage the situation for their team by playing cautiously against the charged up Indian pacemen who bowled a tidy line and length.
But Pathan struck again by claiming the wicket of Younis Khan (12) with Yuvraj Singh latching on to a smart catch, allowing the Indians to take a tight control of the proceedings.
With the hosts reeling at 58 for four by the 13th over, it was left to Inzamam, who had hit two centuries in the previous matches of this high-profile series, to pull the team out of the pits and the burly captain seemed to be in no discomfort as he went about the task of rebuilding the innings with a cool head.
Inzamam curbed his attacking instincts and was quite content in keeping the scoreboard ticking with singles but as a result the asking rate kept mounting.
The Pakistan captain and Shoaib Malik put on 29 runs for the fifth wicket before left-arm spinner Murali Kartik claimed the prized scalp of Inzamam.
The right-handed Inzamam tried to lift Kartik out of the ground but Sachin Tendulkar latched on to a brilliant catch just a few inches inside the boundary line at the long-on fence. He scored a 51-ball 38 that contained five boundaries.
All-rounder Abdul Razzaq (5) also could not hang around for long, falling prey to Balaji as he returned for the second spell from the far end.
Then came the most productive period for the home team as Shoaib Malik and Moin Khan raised hopes of a spirited fightback with a 99-run seventh wicket partnership.
As the evening progressed, the dew made it difficult for the bowlers to grip the ball. Both Malik and Moin took advantage of the situation and played some attacking shots in a bid to accelerate the pace of scoring as the run rate had climbed to more than seven runs at that stage.
Part-timer Virender Sehwag finally brought the flourishing partnership to an end by scalping Malik for 65 that came off 89 balls.
Moin and Mohammed Sami kept up the run chase with a rollicking 52-run partnership, making the visitors a little panicky, but it was too uphill a task by then.
Earlier, put in to bat after Inzamam won the toss for the fifth time in a row, VVS Laxman, awarded Man of the Match, marked his return to form with a scintillating 104-ball 107 to propel India to a competitive 293 for seven which also saw some lusty hittings by the tailenders.
The stylish Laxman, who did not have a big score to his credit in the three earlier matches, notched up his sixth One-day century, his fourth this year, as he paced his innings brilliantly after the visitors lost both their openers Sehwag and Tendulkar rather early.
Captain Sourav Ganguly was the second highest scorer with 45 but it was the late charge by Pathan (20 off 12) and Balaji (10 off 6) that gave some respectability to the Indian total.