Chasing a modest victory target of 153 on Wednesday, West Indies did not lose a wicket, and Gayle had the privilege of hitting the winning runs in the first day-night ODI in the Caribbean, when he drove Prosper Utseya through extra cover for the last of his 13 fours.
Gayle also hit a six in his undefeated 95 - the top score - at better than a run-a-ball to earn the Man-of-the-Match award, and Chattergoon supported with eight boundaries in an unbeaten 54 from 78 balls to give West Indies an unbeatable 4-0 lead in the seven-match series.
All-rounder Dwayne Bravo and compatriot Dave Mohammed had wrecked Zimbabwe's batting to leave West Indies their modest target.
Bravo captured three wickets for 24 runs from 9.2 overs while Mohammed collected three for 37 from 10 overs on his ODI debut, as the Zimbabwean were dismissed for 152 in 49.2 overs after choosing to bat.
Diminutive batsman Gregory Strydom cracked four fours and two sixes in the top score of 48 from 73 balls.
Zimbabwe captain Terrence Duffin gave support with a painstaking 38 and Brendon Taylor gathered 21 at close to a run-a-ball.
Gayle and Chattergoon were never troubled and carried West Indies safely to their destination.
Gayle reached his 50 when he steered Tawanda Mupariwa to third man for two in the 19th over and continued to clobber the bowling, especially left-arm spin bowler Keith Dabengwa, who he struck for his only six straight into the players' pavilion.
Chattergoon enhanced his reputation as a player with immense potential with his dogged batting, and reached his half-century, when he played Prosper Utseya into cover for a single in the 24th over.
Zimbabwe never recovered, after Mohammed bowled Vusimuzi Sibanda for four in the 19th over to leave Zimbabwe on 48 for three.
The Zimbabweans had suffered an early setback, when opener Piet Rinke was caught at second slip off Taylor in the second over for his second duck in as many matches.
Brendon Taylor then came to the wicket and with Duffin got things moving before he was caught at mid-on off Bravo for 21 in the 16th over.
Zimbabwe continued to lose wickets steadily, but Mohammed struck two telling blows in the 40th over, when he removed Dabengwa hit wicket for seven and bowled Blessing Mahwire. also for a duck.
Strydom entered during this period and was inching his way to his half-century. adding a valuable 40 with Mupariwa for the eighth wicket, before Bravo removed them both as the last three wickets fell for no runs in the space of six balls.
West Indies enjoyed back-to-back victories by five wickets and 98 runs in the first two matches at St. John's, and an 82-run triumph last Sunday at Georgetown. The third match also scheduled for Georgetown last Saturday was cancelled because of rain.
The series concludes at the weekend with a double-header at Port of Spain's Queen's Park Oval.