The 50-over-a-side match was first reduced to 40 overs , with a further six overs deducted later as Zimbabwe were set a revised target of 225.
Saqlain Mushtaq took four wickets in five balls, including a hat-trick, to spin Pakistan to victory and take the series 3-0.
India beat Australia by five runs in Mohali yesterday with as many deliveries to spare to go through to the final of the Titan Cup.
Chasing India's 290, Australia required six off the last over with the last pair in but Brad Hogg ran himself out on the first delivery.
India will play South Africa in the final of the three-nation tournament on Wednesday in Bombay.