It was Pakistan's first victory of this World Cup after losing by 76 runs to India and suffering a 150-run hiding at the hands of the West Indies in their previous two Pool B fixtures.
Misbah needed his bowlers to set up Sunday's win after his side had been limited to a modest 235 for seven by another poor top-order effort .
It was Pakistan's highest total of the tournament but a long way off the fourteen 300 and over totals so far registered elsewhere in the event.
So far at the World Cup, Pakistan have scored 224 all out against India and were dismissed for just 160 by the West Indies.
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Misbah has his team's best two scores of 76 against Pakistan and 73 on Sunday.
Umar Akmal and Sohaib Maqsood got beyond fifty against the West Indies while Wahab Riaz scored a half-century against Zimbabwe at Brisbane's Gabba ground.
"It was really tough because it was a make or break game for us. You can't believe how happy we are because we were out of the tournament if we'd lost this game," added the captain.
"I felt 250-260 would be really challenging today. We were 15-20 runs short but we showed the kind of quality we have in the bowling line-up and credit should be given to the fast bowlers.