Ofoyrwoth managed three penalties and a drop goal to tally 12 points for the Heathens, while Nobert Okeny scored the game's only try.
After falling 24-18 to Stanbic Black Pirates in the season's opening game, Platinum Credit Heathens were left in a spot of bother.
Defending the league starts and ends with beating Pirates and Kobs, but two games into the season, Muhammad Athiyo's charges had already fallen behind in the race.
The game against Kobs at Legends became a must-win for the Yellow Machine to stay in the title race.
And the manner in which Heathens won the game only emphasized the giant of a club they are, Aaron Ofoyrwoth, the hero on the day.
With Kobs destined for what looked like a slim 15-14 win after Joseph Aredo split the uprights from a penalty late in the game, Heathens stayed alive in the title race.
Ofoyrwoth collected Daudi Ssemwami's clearance kick, set himself and went for a last-ditch drop goal to hand the visitors the victory in dramatic fashion on enemy territory.
A largely dull affair at Legends only came to life in the closing stages.
Kobs were carried by Joseph Aredo's splendid boot that converted five of his six penalty attempts.
Ofoyrwoth managed three penalties and a drop goal to tally 12 points for the Heathens, while Nobert Okeny scored the game's only try.
That was on Match Day Three. Kobs have yet to drop any other game since then, defeating Pirates 30-25 in a highly-billed affair at Kings' Park to ascend to the table.
The Blue Army are now on 55 points and on top of the log, while Heathens lead the chasing pack, just a point behind the leaders.
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09:11 - 28.03.2023
RUGBY How Rugby League table looks like after 12 rounds
Brian Makalama’s Kobs continue to lead the way after 12 rounds of games with a massive 55 points and a points difference of 412.
The two rivals will face off on Saturday in what could be the title decider.
Heathens are without Ofoyrwoth, Michael Wokorach and Okeny. The trio is part of the National Sevens team.
Charles Uhuru is also out for the entire season after he was handed a lengthy ban for dangerous play against Adrian Kasito in the win over Kobs.
Brian Mkalama's side, meanwhile, are depleted. Kasito, Ian Munyani and Mark Osuna are with the Uganda Sevens team.
At the same time, Pius Ogena, Jude Jjuuko and Faragi Odugo are part of East Africa RFC in Hong Kong for the Hong Kong 10s tournament.
But it never matters who wears the jersey when Heathens and Kobs meet.
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