After winning the toss and electing to field first, India bowled out Pakistan for 147 with fast bowler Bhuvneshwar Kumar taking 4-26. Wicketkeeper-batsman Mohammad Rizwan shined with the bat for Pakistan with 43.
In reply, India's batsmen recovered strongly after an early wobble to chase down their target with just two balls to spare.
Cricket's biggest rivals were greeted by a packed stadium of supporters for both countries.
It was sweet revenge of sorts for India, who went down to Pakistan for the first time in a World Cup match last year at the same venue when the two teams met in the group stages of the ICC Men's T20 World Cup.
India's next match is against Hong Kong on Wednesday, while Pakistan take on the same opponent on Friday, September 2 in Sharjah.
The arch rivals will most likely meet again later in the tournament, in the Super Fours stage and possibly the finals on September 11.
Cristiano Ronaldo became the first player to score in six World Cups and Portugal’s all-time leading marksman at the global finals with two goals in Tuesday’s emphatic 5-0 Group K win over Uzbekistan in Houston.
The United States eased restrictions on the Iran squad's travel arrangements at the World Cup on Tuesday, allowing them to travel two days before their next match, the US Department of Homeland Security said.
Former Lucknow Super Giants captain Rishabh Pant will return to the Delhi Capitals while spinner Kuldeep Yadav will move the other way in a high-profile player trade in the Indian Premier League (IPL), the organisers said on Tuesday.
Algeria stormed back to beat Jordan 2-1 and eliminate the World Cup debutants with a match to spare on Monday thanks to second-half goals from substitute Nadhir Benbouali and Amine Gouiri.
Kylian Mbappe has scored his second double of the tournament as France eased into the last 32 with a 3-0 victory over Iraq on Monday in the first match of this World Cup beset by a lengthy weather stoppage.
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