Pakistan, who restricted India to 245-8, survived anxious moments before Shahid Afridi smashed two consecutive sixes to help his team win with two balls to spare at the Sher-e-Bangla stadium.
India, who have lost two of their three matches, are unlikely to make the March 8 final even if they beat Afghanistan in their last match.
Saeed Ajmal claimed 3-40, while debutant fast bowler Mohammad Talha and Mohammad Hafeez grabbed two wickets each after Pakistan won the toss and elected to field at the Sher-e-Bangla stadium.
Each team has won and lost a game in the five-nation tournament, and the loser will almost certainly be out of contention for a place in the final on March 8.
Opener Rohit Sharma (56) and Ambati Rayudu (58) were the main contributors for India at the top of the order, before Ravindra Jadeja hit an unbeaten 52 off 49 balls towards the end.
Jadeja, who walked in to bat in his 100th one-dayer with his team shaky on 155-5, smashed four boundaries and two sixes to boost the total.
Pakistan got off to a good start by removing opener Shikhar Dhawan and danger man Virat Kohli by the 10th over.
Left-handed Dhawan, who hit 94 against Sri Lanka on Friday, was leg-before to off-spinner Hafeez in the third over for 10.
Kohli, captaining India in the absence of the injured Mahendra Singh Dhoni, was caught behind by Umar Akmal off seamer Umar Gul for five.
Sharma, who fell cheaply for 21 and 13 in the previous two matches, struck timely form with seven boundaries and two sixes in his 22nd one-day half-century.
But just when he seemed set for a big score, Sharma top-edged a catch to give Talha his first wicket and make India 92-3 in the 20th over.
Talha also dismissed Ajinkya Rahane for 23, but was taken off with figures of two for 22 in his first seven overs.
Rayudu put on 52 for the fifth wicket with Dinesh Karthik and 59 for the sixth with Jadeja before he holed out in the deep in the 47th over.
India went into the crucial game with an extra spinner in leg-break bowler Amit Mishra in place of all-rounder Stuart Binny.
