But Adelaide were clinical — and helped by some hesitant, shaky defending — while the Phoenix missed in almost every way possible.
The result leaves Wellington in fifth spot, with a cluster of teams around them.
The Phoenix predictably missed the cutting edge of Oskar Zwada (on paternity leave) though were able to welcome Clayton Lewis and Sam Sutton back from injury for the final 30 minutes.
The Phoenix made a bright start, seeking just their fifth win in Adelaide in 24 matches, before the opening goal came out of nowhere.
It was a gift for the home side, as Oli Sail made a mess of an attempted back pass by Scott Wootton.
As a cross came over his shoulder, the English defender chested it down towards the keeper, but the ball wriggled out of his grasp.
Adelaide extended their lead seven minutes later, with another messy goal.
After the Phoenix couldn’t deal with a Craig Goodwin free kick, the ball pinged around the penalty area, until it was forced home by Luka Jovanović.
Wellington had played more football, but Adelaide’s pressing and physical intensity was making the difference.
To their credit, the Phoenix responded, dominating the rest of the half.
Yan Sasse forced a point-blank save from Joe Gauci — after neat buildup play from Bozhidar Kraev — before the Bulgarian was narrowly wide with a near-post flick.
Kosta Barbarouses also missed a glaring opportunity, in an episode destined for end-of-season blooper reels.
The All Whites striker showed great awareness to rob Gauci near the byline, but then poked his shot onto the far post, with the goal gaping.
It was a narrow angle but Barbarouses lacked his customary composure.
The frustration continued early in the second half with a double whammy: first a Kraev shot slipped just wide of the woodwork, then Lachlan Barr thundered a header home for Adelaide’s third from another perfect Goodwin delivery.
Rufer’s penalty finally got Wellington on the board after Sasse was tripped in the box.
After enduring 107 matches before his first A-League goal, Rufer only had to wait seven matches for his second.
But the joy was short-lived as substitute Hiroshi Ibusuki grabbed Adelaide’s fourth after a quick counter, before Goodwin cut inside to net a fifth.
Wellington Phoenix 1 (Alex Rufer pen’ 54′)
Adelaide 5 (Scott Wootton OG 16′, Luka Jovanović 23′, Lachlan Barr 51′, Hiroshi Ibusuki 62′, Graig Goodwin 71′)
Halftime: 0-2