Wellington exposed the Bay defence in the sixth minute through homeboy Andy Bevin, whose 45-degree cross from the left flank found striker Ben Harris lurking before the right upright to score what was perhaps his easiest goal this summer, for 1-0.
Twenty minutes later Wellington right winger Luis Corrales took matters into his own hands when centreback Harrison Nash's wild kick took him off his feet, but referee Chris-Kerr Waugh showed him a yellow.
The controversial equaliser, 1-1, came in the 47th minute when leftback Sean Liddicoat casually tapped the ball about 2m in front of the left upright amid suggestions he was "miles offside". However, there was a cryptic message in that tap-in goal because, offside aside, it screamed "cross the flaming ball" after Tom Biss took it to the goal line but, trying to dribble past a defender, lost possession. Wing back Kohei Matsumoto dutifully crossed it past the goalmouth.
The hosts went up 2-1 in the 56th minute when right-mid Birhanu Taye followed up centre-mid Zane Sole's pile-driving freekick from about 35m out.
Basalaj spilled the ball and Taye followed up for a sweet doughnut between the keeper's leg.
But that euphoric edge only lasted four minutes when Wellington levelled terms, 2-2, from a Harris penalty kick after Bay captain Finlay Milne tackled Saul Halpin from behind.
"That was the disappointing thing, going 2-1 up ... , " he said, unsure if the penalty kick was actually one but feeling the goal took the zing out of the game.
Ifill said they had to take "the rough with the smooth and move on" when asked about Bay's first goal: "I'm not going to have a go at the referees but I think some of the decisions were questionable although I think they went both ways."
Both Harris and Bay counterpart Sam Mason-Smith asked the crossbar questions, without joy.
Ifill's impact was undeniable, putting Hamish Watson through on the left flank over centreback Bill Robertson's head, but the substitute striker couldn't capitalise.
Into added time, Watson had a difficult chance to glance in an Ifill shot but the ball ricocheted off his head.
"The other way to look at it is that it is important not to be beat [sic]," he said, mindful Team Wellington remain a point above them and Bay United have two games coming up on the road.
"It's important to go down to Canterbury [this Sunday] and Southern [January 24] to get points so we're still in the mix in the top four."
Napier-born defender Fergus Neil said he relished playing at Bluewater Stadium in a Wellington outfit that included other Bay or ex-Bay connections in Robertson, fellow co-captain Cole Peverley - who pulled out at halftime after vomiting - midfielder Bevan, Englishman Saul Halpin and last summer's midfielder, Argentine Mario Barcia.
"It was scrappy at times but, I think, we're disappointed to have drawn after we were up 1-0 at halftime," he said, reconciling that with how they returned to equalise from 2-1 down.
"You can't be too displeased getting a result away at Hawke's Bay because it's a tough place to come. It's a special game for all of us who have played here, I guess."
Neil said Wellington were "a little bit unlucky" to concede the first goal: "Obviously the lino [ref's assistant] put his flag up and then put it down after everyone had stopped playing so we sure were a little hard done by but that's football."
