The Kent Forester League Division One match saw Andy Cronin and Andy Watts take impressive figures of 4-29 and 4-76 at the home team bowled the visitors out for 173.
Blackheath then took to the crease to chase Gravesend's modest total and made light work of it as Paul Frith hit a sparkling unbeaten innings of 89 and Raj Bhandari hit 56. Blackheath finished the match on 173-3 to win by seven wickets.
Blackheath travel to Canterbury next week.
Meanwhile, RACS slipped to their first loss of the season in a disappointing home defeat against Whitstable on Saturday.
RACS batted first at Sparrows Lane but could only reach the modest total of 147-4. Rob Archer starred with an innings of 45.
Whitstable in turn reached 148-8, despite A Tutts' impressive bowling figures of 5-74, to win by two wickets.
RACS are again in action at Sparrows Lane next week, this time against Hayes.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article