The Dutchman scored from inside his own half but it was the visitors who went home with all three points after notching in each half to revive their top-two hopes
Kim Seung-Yong's equaliser in first-half injury time and a second-half winner from substitute Bernie Ibini sealed all three points for the reigning champions, giving themselves a healthy four-point buffer over seventh-placed Sydney FC with three rounds of the regular season remaining, and the race for finals places hotting up.
For Heart meanwhile it is still not mathematically impossible to finish in the top six, but John van 't Schip's team, ninth in the standings and seven points back from the Newcastle Jets, would need to win all their remaining fixtures and hope for some major collapses from their immediate rivals.
One of the most uninspiring opening 30 minutes to a game this season may have left some members of the sparse crowd asleep in their seats, with Heart threatening only twice and the Mariners not at all.
In the 20th minute Eddy Bosnar slipped to let in David Williams, who shot high and wide, while 10 minutes later Zach Anderson did well to clear Mate Dugandzic's cutback off the line, denying Iain Ramsay a tap-in.
If any fans did nod off, they could be forgiven for doing so, but would then have been in danger of missing a goal which will go down in A-League history.
In the 34th minute Engelaar, gaining possession just inside his own half, looked up and spotted Liam Reddy off his line, dispatching an extraordinary, perfectly weighted shot which left the goalkeeper helpless.
It could not have been from less than 55 metres out and is yet another feather in the cap of the Dutch marquee, who has impressed greatly since recovering from the broken leg which delayed his debut in the competition.
Heart could have made it 2-0 when fullback Ben Garuccio cut in from the left flank and slipped a dangerous ball into the six-yard box, which Williams narrowly failed to tuck home.
The Mariners, having comprehensively failed to threaten throughout the half, summoned something from nothing in injury time.
Mat Simon appeared to obstruct Patrick Kisnorbo to allow Mile Sterjovski to nod on a hopeful long ball, and Kim collected it at the back post, cutting inside Jason Hoffman and curling a cool finish beyond Andrew Redmayne.
Heart made the running early in the second term, but it took until the 57th minute for a decent opportunity to arrive, when a Robbie Wielaert through-ball played Williams in on goal, only for Reddy to produce a good low save.
Four minutes later and Williams went close again, drawing another save from Reddy after meeting Dugandzic's cross with a firm header.
The goalkeeper was also called on in the 73rd minute, parrying a header from substitute Harry Kewell at the back post.
Despite Heart's sustained pressure, it was the Mariners who made the all-important breakthrough.
With 13 minutes to go, Marcel Seip headed a ball into the path of Ibini, who raced in on goal and slotted past Redmayne to give his team the lead.
There were half-chances for Heart to snatch an equaliser in the remaining minutes, but the hosts proved unable to breach the title-holders' defence when it mattered most.
With a week off from AFC Champions League duty, the Mariners will now prepare for a home game against Western Sydney next Saturday, while Heart go away to tackle newly crowned premiers Brisbane Roar a day earlier.
Melbourne Heart 1 (Engelaar 34')
Central Coast Mariners 2 (Kim 46', Ibini 77')