Ghulam made his name with a hundred in his debut Test against England at Multan last month, and this time cracked 103 off 99 balls on Thursday in a strong Pakistan total of 6-303.
Zimbabwe then capitulated for 204 in 40.1 overs as Pakistan captain Mohammad Rizwan used seven bowlers, with only off-spinner Salman Ali Agha not among the wickets.
A second successive ODI series win for Rizwan followed an historic 2-1 victory in Australia, Pakistan's first there since 2002.
In the absence of rested fast bowlers Shaheen Shah Afridi and Naseem Shah, Pakistan's second-string pace attack did fairly well in Zimbabwe as the visitors prepared for next year's Champions Trophy at home.
Fast bowler Aamer Jamal (2-19), who made his ODI debut in the series, peppered Zimbabwe with short deliveries and claimed Craig Ervine (51), who dragged onto his stumps shortly after Tayyab Tahir dropped a sitter off the top-scoring Zimbabwe skipper at midwicket.
Jamal also picked up the key wicket of Sikandar Raza (16), who pulled the pacer to deep square leg to give Abdullah Shafique an easy catch.
Brian Bennett counter-attacked with two sixes and four boundaries in 37 off 27 balls but the Zimbabwe tail folded meekly. Bennett scooped an easy catch to short fine leg against leg-spinner Abrar Ahmed (2-45).
Zimbabwe shocked Pakistan with an 80-run win in the first ODI but the visitors bounced back with a thumping 10-wicket victory on the back of Saim Ayub's scintillating 113 off 62 balls.
Ayub continued where he left of on Tuesday. The left-hander smashed three fours and a six in his 31, but he couldn't clear the midwicket boundary and was caught by Clive Madande.
Ghulam laid the foundation for a big total by combining for 54 with Abdullah Shafique (50) and 89 with Rizwan, who scored 37.
Ghulam used his feet well against the spinners and reached his century when he pulled Sikandar Raza through midwicket for his 10th boundary.
Ghulam lasted for three more deliveries before he was deceived by a slower delivery from fast bowler Richard Ngarava and holed out at deep cover in the 45th over.
Pakistan profited from wayward bowling at the death as Tayyab Tahir hit 29 off 16 balls and vice-captain Salman Ali Agha made 30 off 26. Pakistan scored 69 off the last five overs and Faraz Akram conceded 23 in one over.
The teams begin a three-match Twenty20 series on Sunday.
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