Nixon hits the winning run for Abbots off the final ball
Rain delays reduced the match to 33 overs and both sides found it difficult to score.
The hosts lost wickets frequently and were on 85-5 at one stage, before closing on 137-6.
Matt Dunstone took three wickets.
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Hide AdAbbots slipped to 43-4, before Bradley Finch (47) and skipper Matt Parkins (32) steadied the ship to leave Abbots needed seven runs off the last four overs. But they lost three quick wickets, with Abbots needing four runs off the last five balls.
Anish Khiroya ran a two and then a single off the penultimate ball, leaving Nixon to face the last ball.
He connected to split two fielders to take the winning run.