The midfielder scored with a 30-metre piledriver with three minutes remaining to complete an impressive turnaround from Brisbane.
Teenage Brisbane debutant Devante Clut had earlier equalised with a brilliant strike of his own, following a first half goal from Stein Huysegems that was a just reward for Wellington's strong showing early in the match.
The Phoenix came into the game with a record of five losses and a draw in their previous six encounters with the Roar but did not look overawed in the slightest as they bossed proceedings from kick-off.
For much of the first half, Phoenix held a rigid formation in defence to stifle Brisbane's attacking threat, and looked dangerous themselves when breaking forward.
Following Huysegems' goal, however, the home side began to turn things around and find ways through a previously impenetrable Wellington backline.
Vince Lia cracked an effort against the upright in the 11th minute after some slick build up play by the Phoenix around the Roar area.
Huysegems nearly laid on a goal when he executed a delightful turn on the edge of the box before laying the ball on to Jason Hicks, whose stinging low shot was pushed around the post by Michael Theo.
Jeremy Brockie came close to scoring a freak goal when he forced a save from Theo with a low volley from an acute angle on the left.
Wellington claimed a fortunate, but deserved goal when Brockie's scuffed shot slid past Brisbane's central defenders only to end up at the feet of Huysegems, who bundled the ball over the line from close range in the 36th minute.
The Roar mounted something of a first-half fightback, as Dimitri Petratos tried a long-range effort which was parried by Glenn Moss.
Henrique then missed an absolute sitter when he failed to turn in a low Jack Hingert cross at the near post.
The Brazilian import came close to winning a penalty moments later when he was fouled by Michael Broxall right on the edge of the area, but the referee correctly awarded a free kick rather than a penalty, and the Roar were unable to make anything from the chance.
Thomas Broich then tried to take matters into his own hands, showing excellent close control to evade two defenders before sending a 25-metre shot thundering against the crossbar.
The Phoenix survived the late Brisbane surge, however, and went into the break with a one goal lead.
Five minutes into the second half, Clut marked his debut with a spectacular goal as Broich's cross was laid on by Henrique with his chest and the teenager took one touch before rifling a shot into the top left corner of the net from just outside the box.
The German continued to impose his talent on the game, floating a superb cross in for Henrique who could not quite leap high enough to make meaningful contact.
Henrique then raced into space thanks to a Petratos through ball but Moss raced out of his area to stifle the chance in the nick of time.
Diogo Ferreira's shot was blocked by Moss and Petratos nipped in to bury the rebound, only to have the goal disallowed for offside, as Brisbane stormed forward in search of a winner.
The Roar hit the woodwork for a second time from a corner when Henrique tried an overhead kick in a crowded area and his shot was deflected onto the crossbar .
Brattan's astonishing winner came after a Phoenix defensive clearance, with the midfielder taking a long run up and cracking the ball in from 30 metres, with the help of a slight deflection off the boot of the unfortunate Vince Lia in what proved to be the decisive moment of the match.
Brisbane Roar 1 (Clut 50, Brattan 87)
Wellington Phoenix 1 (Huysegems 36)
Crowd: 13,889 @Suncorp Stadium
