But as an under-manned Wellington pressed for a late equaliser, Perth striker Bruno Fornaroli scored an eye-catching tenth goal of the season to confirm the points for the home side.
Having not won in Western Australia since October 2015, the Phoenix travelled early in the week and that move seemed to pay off with their now familiar passing game in evidence from the opening whistle. However, unlike previous weeks, there was a lack of cutting edge in the final third.
Despite shading first-half possession, the Phoenix were unable to fashion regular openings, with the best chance falling to David Ball who flashed his left-footed effort wide from a narrow angle after a scything run from Reno Piscopo.
Having defended stoutly for most of the first half with centre-backs Steven Taylor and Luke DeVere particularly prominent, the Phoenix were hit with a double-punch in the shadows of halftime.
Defender Tomislav Mrcela opened the scoring with a close range header after Wellington failed to defend a whipped left wing corner.
Worse was to follow in stoppage time with Olyroos striker Nick D'Agostino tucking away the second after clever buildup work from Joel Chianese and Fornaroli.
D'Agostino extended the lead ten minutes into the second half, heading home his second after a precise left-wing cross from Kim Soo-Beom.
The third goal was the catalyst for Hooper's introduction with the former Premier League striker twice showing his class in the penalty area. However, Wellington had left themselves with too much to do, Fornaroli's late curling effort snuffing out any chance of a share of the points.
Phoenix coach Ufuk Talay will have to refocus his troops quickly – and find a replacement right-back – ahead of their clash with another of the A-League's high-fliers, second-placed Melbourne City at Eden Park next Saturday.
Perth Glory 4 (Mrcela 43', D'Agostino 45 + 1', 54', Fornaroli 90')
Wellington Phoenix 2 (Hooper 68', 76')
