Haviland received a red card as the last defender and he was joined in the changing rooms soon after by another ex-WaiBOP United player in Chad Coombes, who received a second yellow.
Meanwhile, WaiBOP captain and defender Adam Mitchell was stretchered off in the second half with a dislocated shoulder.
Thursday's result sees WaiBOP United, who recorded a 5-1 win over Waitakere in November, jump up to second on goal difference while Waitakere United remain in sixth position, six points outside the top four.
WaiBOP United coach Peter Smith paid tribute to his side, who were braced for a strong effort from the visitors.
"The lads did extremely well," Smith said. "We had a game plan, the lads stuck to the game plan and the system we're playing suits the abilities of the players we've got.
"In the middle of the park we won the battle there. Alexis Varela, Mario Ilich and Federico [Marquez] worked extremely hard with Mark Jones and Sean Morris coming in and supporting them.
"The result we had against Waitakere at the start of the season, they would be desperate to avoid that. We were aware they'd come with a bit of fight and a bit of spirit and [we had] to prevent that."
After their third straight win, Smith said the team are flowing with the confidence that such a streak provides.
"When we spoke a few weeks ago we said the next three games were must-win games if we wanted to be in the playoffs. To get the result against the Phoenix, to back that up against Southern and to get the result and the performance tonight it indicates we're in a good space. But at the same time we're taking nothing for granted."
Waitakere United coach Chris Milicich lamented a poor defensive outing from his side in a crucial game.
"[It] certainly wasn't the result we were looking for," Milicich said.
"I thought we were done by some pretty simple long balls over the top of us, we didn't defend it well. Waikato have played well, they scored their goals...we had chances but we were by far the second best side tonight."
Milicich said his side will keep fighting for their playoff lives but said he would look at freshening up his team for their next match.
"Mathematically there's a chance there, and you always keep playing while there is a chance. It would be fair to say there will be quite a few changes coming through, there kind of has to. It's not an acceptable result with two guys getting sent off.
The ASB Premiership continues on Sunday with three matches: Southern Utd v Hawke's Bay Utd, Team Wellington v Canterbury United and, in the SKY Sport televised encounter, leaders Auckland City take on the Wellington Phoenix.
