The Londoners bossed the match for long periods but fell short in the main due to a superb individual performance from Haven player-coach Carl Forster who marked his 100th appearance for the club with tries either side of half time and an assist for James Newton two minutes from the final hooter.
Jesse Joe-Parker crossed for Haven prior to Newton while Paul Crook was spot on in front of goal with successful kicks.
The result saw third-placed Haven move to within two points of Division One pacesetters Toronto Wolfpack and Barrow Raiders.
Haven were out of sorts early on and looked to have shipped the first try of the afternoon when Skolars right wing James Hill won a foot race against Elliot Miller, only to have his third-minute effort chalked off as he took the ball in an offside position after team-mate Jy-mel Coleman had created the opening with a long kick from deep in his own half.
Skolars, however, did get the scoreboard ticking on seven minutes when Josh Allison held off three Haven defenders to crash over the try line in the same spot as Hill had done moments earlier.
Coleman failed to add the extras but Skolars kept up the pressure and only a last ditch monster tackle by Elliot Miller stopped a certain try by Will Martin under the posts on the 20-minute mark.
After a period of non-stop defending, Jordan Burns and James Newton finally fashioned an opening down the left wing for Haven, only to be thwarted by Skolars centre Kameron Pearce-Paul.
Back to back penalty awards though then sent Haven rolling forward and Newton found a killer pass enabling Forster to crash through two Skolars defenders and under the posts after 28 minutes play.
Crook slotted the extras but Skolars had the upper hand and edged back in front when Coleman recycled the ball close to the Haven line, Allison fed Hill who touched down in the corner just after the half hour.
Coleman failed with his kick from the right touchline.
Haven in terms of stats were down on possession and yardage throughout the half, and could count themselves fortunate to be only 8-6 down at the break.
Skolars had been the clear aggressors and Forster had work to do in his half time pep talk.
Leading from the front, Forster himself put Haven back ahead in their first attack of the half, crashing over from close range three minutes after the resumption.
Crook slotted the kick for a four-point advantage.
Buoyed by the score, Haven at last enjoyed more possession, though defences were up for this challenge to keep an enthralling clash in the melting pot well into the last quarter of the game.
Haven left wing Joe-Parker had been stymied throughout the game through tight marking but neatly side stepped away from his marker to touch down behind the posts for a terrific solo score on 66 minutes.
Crook added the kick for an 18-8 advantage and kicked his team further ahead from a penalty following a late tackle on Roper nine minutes from time.
But, if Haven thought the match was over they were wrong as Skolars, needing the next score, duly got it courtesy of a short drive to the line from forward Sadiq Adebiyi in the 74th minute.
Coleman slotted the two points to reduce the Skolars deficit to a converted score.
But Forster, who else, had the final say punching the air in triumph after breaking through the London defence to send Newton in for the match winning score.
Crook slotted the conversion, then a late penalty but it had been a close call.
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 here