The tourists, bowled out for a modest 177, hit back to dismiss Bangladesh for 119 on a wicket that turned and bounced at the Zahur Ahmed Chowdhury stadium in the port city of Chittagong.
"This was a really tough game," Misbah said. "But when there is self-belief you manage to get through.
Shoaib Malik marked his 200th one-day international appearance with three wickets for six runs in his four-over spell and his fellow off-spinner Mohammad Hafeez picked up three for 27 as the Tigers were bowled out short of victory in 38 overs.
It was Pakistan's 28th win in 29 one-dayers against Bangladesh, boosting the confidence of Misbah's men ahead of the two-Test series starting on Friday.
Bangladesh were sailing smoothly at 69 for one in the 20th over when five wickets fell for 14 runs to allow Pakistan to bounce back and win.
"Our bowlers did wonderfully well but we need to improve our batting," Misbah said.