The hosts won Saturday's first game by eight wickets and though they batted first on Sunday, they had no problem repeating the result after amassing 158 for seven.
Lendl Simmons set them on their way, following up Saturday's unbeaten 63 with an innings of 41, but it was Pollard who stole the show by hammering 45 not out from only 24 balls.
Zimbabwe were never in the hunt despite Hamilton Masakadza's unbeaten 53, Samuel Badree taking three for 17 as they stumbled to 117 for six.
After West Indies captain Darren Sammy won the toss, Simmons lost opening partner Johnson Charles with only 19 on the board but found support from Dwayne Bravo (24) in a second-wicket stand of 42.
Christopher Barnwell made just seven but Pollard launched three sixes and three fours as he and Sammy, who hit 19 from 12 balls, put on a blistering 56 in 4.2 overs. Ducks for Andre Russell and Denesh Ramdin could not halt their side's momentum, and nor could two wickets apiece for spinners Natsai Mushangwe and Tinotenda Mutombodzi.
Badree removed openers Chamu Chibhabha and Vusi Sibanda and added the scalp of captain Brendan Taylor to leave Zimbabwe 33 for three in the eighth over.
Masakadza put on 35 for the fourth wicket with Craig Ervine, who made 15 before offering up a return catch to Bravo.
The run-out of Max Waller ended a 23-run fifth-wicket stand and Mutombodzi became Bravo's second caught-and-bowled victim in three overs that brought him two for 15.
Masakadza's half-century came up with successive boundaries off Russell, his fifth and sixth in a 51-ball effort, but though Prosper Utseya (11no) plundered a boundary in the last over the target was comfortably beyond Zimbabwe's reach.