Four minutes from the end of the spell, Emiliano Tade ran on to a neat ball slipped through by David Mulligan to whip it home hard and low.
Down, but far from out, the visitors set the second half alight when Michael White scored after three minutes and Ethan Galbraith, who had an intriguing battle with Ivan Vicelich throughout, headed home for 2-2.
City needed almost 20 minutes to score the go-ahead goal when Luis Corrales continued his amazing scoring record against the southerners with a well-angled effort. Four minutes later Manel Exposito sealed the points when he beat an attempted challenge before unleashing a rocket.
"It was some game. We need challenges like this," said City head coach Ramon Tribulietx. "At 2-2 they were pressing really well."
New Team Wellington boss, Matt Calcott, rued a "couple of lapses" which hurt his team. "We just have to back ourselves more in the first 30 minutes. We switched off at crucial times," said Calcott, who could take heart in what his young team showed.
"It was a big step-up for us after playing Otago first-up."
The two games in the South Island followed a similar pattern with Waitakere and Canterbury racing to 3-0 halftime leads.
Waitakere, enjoying the space at the Forsyth Barr Stadium, went on to add another three after the break, with Allan Pearce scoring two to take his tally to three as he attempts to defend the golden boot he won last season.
Already that is under threat as Canterbury's new signing, George Slefendorfas, banged in four to take his tally after two games to six.
Disconcertingly, next best of the scoring table are own goals - four in the opening two rounds.
In Napier, in a game in which all goals were scored in the second half, Hawkes Bay United and YoungHeart Manawatu picked up their first points with a 2-2 draw.
