Wahab Riaz also excelled with both bat and ball, scoring a crucial half-century and taking four wickets, as Zimbabwe were all out for 215 in the 50th over, chasing Pakistan's 235-7.
It was Pakistan captain Misbah-ul-Haq's patient 73 and a quickfire unbeaten 54 from Riaz that gave the team, looking for their first win after defeats to India and West Indies, a total to defend after losing early wickets to paceman Tendai Chatara.
Zimbabwe openers Chamu Chibhabha (nine) and Sikandar Raza (eight) also found the going tough as both failed to manage rising balls from Irfan, who stands a lofty 2.16 metres (7-foot-1-inch) tall.
The left-armer returned in his later spells to also dismiss Hamilton Masakadza (29) and Solomon Mire (eight) to bag his best figures of 4-30 in ODI cricket.
Brendan Taylor (50) gave the Africans a good platform for the chase with a 52-run stand for the third wicket with Masakadza and then a 54-run partnership with Sean Williams (33) but his dismissal off Riaz brought Pakistan back in the game.
Riaz (4-45) then picked up Craig Ervine (14) and Tawanda Mupariwa (zero) in the space of three deliveries in his eighth over to put the chase beyond Zimbabwe's reach.
Earlier, Chatara (3-35) got ample movement and bounce off the surface to send back openers Nasir Jamshed (1) and Ahmed Shehzad (0) in his first two overs after Misbah had won the toss and opted to bat.
The double blow forced Pakistan to retreat into a defensive shell, amassing the lowest tally in the first 10 overs at this World Cup when they reached 14-2 after the opening 60 balls.
Pakistan were never able to break free at any time in their innings and as is often the case, Misbah was left with the responsibility of rebuilding Pakistan's innings.
The 40-year-old right-hander added a pedestrian 54 for the third wicket with Haris Sohail (27) and 69 for the fourth with Umar Akmal (33) before Williams struck another double-blow to peg Pakistan back.
The left-arm spinner got deliveries to straighten and clean bowled Akmal and birthday boy Shahid Afridi for a duck in the space of three balls.
Misbah holed out at long on trying to clear Chatara out of the ground after another meaningful stand of 47 with Wahab Riaz (54 not out) for the seventh wicket.
The partnership took Pakistan past the 200 mark and some clean hitting from Riaz, who belted six fours and a six in his 46-ball knock for his first 50 in the format, added some vital runs at the death.
(Reporting by Sudipto Ganguly in Mumbai; Editing by John O'Brien and Pritha Sarkar)
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