Medium pacer Tony Russo turned in an impressive 9.2 overs for Greytown, finishing with the excellent bowling figures of 3-22.
Gordon Reisima gave good support with 2-26 from seven overs.
Greytown openers Jake Ross (27) and Paul Lyttle (58) got their team off to a flying start in the run chase.
Lyttle struck 11 fours in his 61-ball stay at the crease and his partnership with Ross was worth a valuable 78 runs.
However, the defending champions made hard work of it from then on and only got home with two wickets to spare.
Skipper Tim Lucas was 27 not out when victory was achieved.
Burling registered superb bowling figures for Red Star, taking 5-27 from his 10 overs, while Sean Jarvis chimed in with 2-39, also from 10 overs.