The Heart's hopes of reaching the A-League finals appear all but over after they gave up a lead at AAMI Park on Sunday.
Engelaar opened the scoring after 34 minutes with a stunning strike not dissimilar to the one scored by Manchester United's Wayne Rooney in the Premier League less than 24 hours earlier.
After spotting Liam Reddy off his line, Engelaar unleashed an effort from inside his own half that flew over the back-pedalling goalkeeper and into the net.
However, the Mariners responded well to claim three points and move up to fourth in the table.
Kim Seung-Yong levelled in first-half injury time, cutting inside Jason Hoffman and curling a cool finish beyond Andrew Redmayne.
And despite Melbourne making much of the running thereafter, the visitors claimed a 77th-minute winner as Bernie Ibini-Isei latched on to a header from Marcel Seip before finishing calmly.
The Heart are now seven points off the top six with three games of the regular season remaining.
Western Sydney Wanderers climbed up to second in the table with a 3-0 home victory over Perth Glory in Sunday's other fixture.
Jerome Polenz put the Wanderers ahead two minutes before the break, firing home at the second attempt after an initial effort had been blocked.
Second-half strikes from Mark Bridge and Tomi Juric sealed a comfortable win for Tony Popovic's men.
Bridge made it 2-0 after 61 minutes with a fine run and finish, while Juric added a late third following good work from substitute Shinji Ono and Youssouf Hersi.
