Fakhar led Pakistan's chase with a freewheeling 81, which earned him player-of-the-match award, but fell short of a hundred trying to wrap up their chase early.
Sri Lanka and the Netherlands can also join them in a mid-table logjam should both win their next games.
Fakhar said the mood was upbeat in the dressing room despite the uncertainty around the 1992 champions making the last four in the showpiece 50-overs tournament.
"In the World Cup, each win gives you confidence and we were waiting for this win.
"We are in the ifs-and-buts (zone) right now - but we will try to win both the remaining matches with good run rates.
Persons:
Pakistan's, Zaman, Sri Lanka's Pramod Madushan, Christopher Pike, Fakhar Zaman, Fakhar, Amlan Chakraborty, Michael Perry
Organizations:
Asia, United Arab Emirates, Sri, Sri Lanka's Pramod Madushan REUTERS, Rights, Bangladesh, England, Thomson
Locations:
Pakistan, Sri Lanka, Dubai, United Arab, Rights KOLKATA, Eden, Afghanistan, Bangladesh, Netherlands, Zealand, New Delhi