Kieran Davies’ last-minute try helped the Yorkshire side secure a much-needed five-point victory – only their second win from eight so far.
Stand-off Davies missed an early penalty, but the Tykes were in the driving seat for the first half hour.
Left winger Harry Jukes touched down on 23 minutes, and centre Ben Dixon added a second try on 30 minutes to put Leeds 10-0 ahead.
Blackheath hit back with a 37th-minute penalty from stand-off Fred Gabbitass, and winger Jake Lloyd touched down shortly after, but Leeds ensured they kept the lead with prop Xavier Valentine crashing over on 39 minutes, Davies converting for a 17-8 lead at half-time.
Shortly after the break the visitors closed the gap with centre Alex Brown touching down, but Leeds continued to keep the scoreboard ticking over with wing forward Dafydd Lloyd scoring on 61 minutes to make it 22-13.
Blackheath enjoyed a purple patch mid-way through the second half which saw them take the lead for the first time.
Tries from Nathan Morris and Steve Leonard put them 25-22 ahead, until Davies raced in with one minute remaining to seal the win for Leeds.
Morley climbed up to fifth in the North One East table after a hard-fought 13-0 win over Pocklington on Saturday.
Goole took a much needed 22-14 victory over hosts Bradford Salem in Yorkshire One.
Previously bottom of the table, Goole climbed up two places to 12th on the back of the three-try victory. But they will need to step up a gear next Saturday when higher-placed West Leeds are their opponents.
Wetherby ran out 29-14 winners from their Yorkshire Two match at North Ribblesdale, the five-point win leaving them second and just two points behind unbeaten leaders Keighley.
Meanwhile, Baildon were 18-3 winners over bottom-of-the table Thornensians.
Moortown will face Sandal in the quarter-finals of the Yorkshire Shield in February after being handed a walkover by hosts Bradford and Bingley on Saturday.
Middlesbrough secured an emphatic 43-19 victory at Wensleydale in the second round of the Yorkshire Silver Trophy to seal a spot in the quarter-finals which will take place in February.
And in the same competition Hullensians and Pontefract reached the second round without a ball being kicked after Bridlington and Leeds Corinthians pulled out of their matches.
Mosborough were 36-14 winners over visitors Richmondshire in their Yorkshire Vase clash on Saturday to book their spot in the next round.
Meanwhile, Burley, Castleford and Ossett all progressed after their opponents decided to withdraw.