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.
Pakistan appointed former captain Sarfaraz Ahmed as head coach of their test team for the two-match series in Bangladesh next month, the country's cricket board said on Saturday.
Coventry City ended their 25-year absence from the Premier League with a 1-1 draw at Blackburn Rovers, securing promotion from the Championship with three games to spare on Friday.
Gujarat Titans adapted to conditions to secure a five-wicket win over Kolkata Knight Riders on Friday, fast bowler Kagiso Rabada said, focusing on tight bowling instead of the explosive batting that has been the hallmark of the Indian Premier League.
Carlos Alcaraz will miss the Madrid Open for the second consecutive year after withdrawing on Friday with a wrist injury, dealing another blow to the world number two's clay court preparations ahead of his French Open title defence.
Novak Djokovic is still working through the injury problems that forced him to miss recent tournaments in Miami and Monte Carlo and said on Friday that he will not feature at next week's Madrid Open, one of the last stops before the French Open.
Dubai Police, in collaboration with the UAE Ministry of Interior, have arrested an Irish fugitive accused of involvement in an organised criminal group linked to international crimes in his home country.
UAE President His Highness Sheikh Mohamed bin Zayed Al Nahyan has met with His Highness Sheikh Hamad bin Mohammed Al Sharqi, Supreme Council Member and Ruler of Fujairah, to discuss national priorities and the country’s continued development.