That could have proved the cue for a nervous final few minutes but the Phoenix closed out the match to win what coach Ufuk Talay had likened to a cup final.
The Phoenix started strongly and their opening 10 minutes of dominance culminated in a goal from Taylor, just his third in the A-League.
A Ulises Davila cross from a quickly-taken corner sailed over three static Roar defenders, with the centre back jumping over the top of Macaulay Gillesphey — like Taylor, a former Newcastle United player — to direct a downwards header just inside the far post.
The rest of the first half was reasonably entertaining but underlined why these two sides (along with the Newcastle Jets) were the A-League's lowest scoring going into this weekend, averaging only a goal a game. The Roar maintained their season-long trend of failing to score in the first half.
Jordan Courtney-Perkins had Brisbane's best first-half chance, placing his shot past keeper Stefan Marinovic six minutes after the opening goal, but a superbly-positioned Taylor cleared the ball off the line.
Six minutes before the break, Alex Rufer did well to drive into the area through the heart of the Roar defence but showed why he is yet to score in the A-League, shooting straight at the Roar's Kiwi keeper Max Crocombe.
In between those two efforts, Liberato Cacace also wasted an opportunity, blazing a shot high and wide after being played in by a great Callum McCowatt pass. But Cacace was otherwise excellent, getting forward particularly well in the first half.
The efforts of Cacace, Rufer, McCowatt, Marinovic and Tim Payne belied their punishing travel schedule to Europe and back during 10 days on All Whites duty.
The Phoenix made a great start to the second half when Davila cut in from the right and then angled a well-placed shot back across Crocombe.
Two goals up, the challenge for the hosts was then to remain composed and not let Brisbane back into the match.
That's what happened when the Phoenix last played two weeks ago in Melbourne, dropping deeper as the match progressed and ultimately failing to defend a lead against the Victory.
Talay partly blamed the pressure of the four-game losing streak for his side's inability to clinch the Melbourne match but will have no such misgivings about tonight's fixture.
There was an awareness that Brisbane represented their best chance of a first win this season, given that due to a quirk of the draw, the Phoenix play four of the top five in December (three for a second time) before first games against fellow strugglers the Central Coast Mariners and Jets in January. Wellington can now look forward to taking on the top sides with a new-found confidence.
Wellington Phoenix 2 (Steven Taylor 10, Ulises Davila 49)
Brisbane Roar 1 (Stefan Mauk 85)
Halftime: 1-0
