Set a modest target of 116 after opting to bowl, Zimbabwe lost early wickets before pulling through in the 13.4 overs courtesy a fine effort by Chigumbura, who remained unbeaten on 53.
Chigumbura struck half a dozen fours and three sixes in his fiery knock, which came off just 21 deliveries. The African side needed to win the match in 15.4 overs to go past Ireland in net run rate to remain afloat in Group B.
Right-handed Chigumbura was the undisputed star of the proceedings, rightly fetching the Man of the Match award for top-scoring in the match.
He got a life in the 12th over when he was dropped by Khurram Khan off medium pacer Manjula Guruge and he capitalised on to it steer Zimbabwe home after a top-order collapse which had reduced them to 34 for four at one stage.
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For the UAE, already out of contention for a place in the main draw, Guruge was the most successful bowler, grabbing 2/18 in his economical four overs.
His 58-run stand with Khurram Khan (26) for the third wicket was the lone steady partnership which the UAE innings witnessed.
Patil struck five boundaries in his knock before being trapped LBW by Sikander Raza, who grabbed two wickets in his three overs which cost merely 15 runs.
The UAE failed miserably to build partnerships after the duo's dismissal and could have found themselves folding up for a less-than-100 score had it not been for a couple of entertaining cameos lower down the order.
Left-arm spinner Sean Williams was once again the pick of the Zimbabwean bowlers, snaring three wickets while conceding merely 15 runs in his quota of four overs.