For an hour, it looked as though the league's form team and best team would cancel themselves out but Engelaar's intervention ensured Heart would meet Melbourne Victory in next week's derby on a winning note.
Engelaar - who combined with Jonatan Germano and ex-Roar midfielder Massimo Murdocca to starve Brisbane of attacking opportunities - opened the scoring for the second week in a row, ghosting into the area to poke in Mate Dugandzic's dink across the box.
Dugandzic looked out of options on the right wing but threaded the ball through the legs of Luke Brattan and found the giant Dutchman unmarked at the far post.
It was a fitting reward for the enterprising Heart who, aside from a quarter-hour in the first half, were better than their table-topping opponents.
Thomas Broich's probing balls were too often missing their targets, while Henrique's trickery in possession made him Brisbane's most dangerous in a lacklustre bunch.
On his first outing in Melbourne since signing for Heart's cross-town rivals the Victory, Besart Berisha was too isolated to test Heart keeper Andrew Redmayne although his dribbling required close attention from marker Patrick Gerhardt.
Gerhardt shaded Berisha through the half until a crunching tackle in injury time that earned him a yellow card, ruling him out of Saturday's derby.
Heart boss John van 't Schip gave Patrick Kisnorbo the Berisha assignment after the break, though Berisha's most notable action was jamming the ball between his legs just six metres from his own goal, meriting an indirect free-kick.
The crowd were highly entertained to see the entire Roar eleven on the goal line, with Henrique blocking the eventual shot.
The Heart endured an inevitable scrappy closing stage - with Kisnorbo making a last-gasp tackle on Berisha in the penalty box - to secure the points.