The 7-6(7) 7-6(7) win over the US Open semi-finalist is only Murray's third ATP-level victory of the year, and he goes on to face fellow Brit Cameron Norrie in the next round.
The former world No 1 beat James Duckworth on New Year's Day before his Australian Open exit in the first round was followed by hip resurfacing surgery.
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And after beginning his comeback on the doubles circuit, Murray's first competitive win in singles came in last week's Zhuhai Championships, where he beat Tennys Sandgren before losing the second round to Alex de Minaur.
But victory over Berrettini on Tuesday marks his biggest win of 2019, while the manner of the win will also be a huge boost for the three-time Grand Slam champion.
Murray was a break down in the first set, but broke back when Berrettini was serving at 5-4 up before taking the opening tie-break 7-2.
The second set saw Murray broken early, but he responded immediately before saving four break points in the sixth game as it headed to another tie-break.
In a topsy-turvy breaker, which featured just seven holds of serve from 16 points, it was Murray who advanced with his first match point after Berrettini failed to convert two set points.
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