Striker Saul Halpin, who scored two goals the previous week, continued his roll with another two yesterday. He scored a field goal in the 12th minute when he beat goalkeeper Coey Turipa after Tasman United's Napier City Rovers player Robbie Pearson had been robbed of possession just outside the 18 yard box.
Eight minutes later the hosts, who were playing their first home game of the season, equalised when classy right winger James Hoyt blasted the ball into the net. Just before halftime Halpin put the visitors ahead with a free kick.
Milne said Halpin's effort was just as spectacular as the previous week's one from a free kick in the loss to Team Wellington.
"Instead of curling the ball around the right hand side of the wall this time Saul did it around the left hand side."
By this stage Turipa had left the field with a shoulder injury and had been replaced by Tom Fawdry.
Tasman United had plenty of possession in the third quarter and Milne said Hawke's Bay United keeper Josh Hill made some crucial saves.
"While Saul was always a threat Josh would have been up with him in the battle for man of the match honours."
On one occasion Hill made a brilliant triple save to deny Dylan Burns and Paul Ifill. Substitute Facundo Barbero scored Hawke's Bay United's third goal in the 82nd minute.
Milne stressed there was still room for improvement from the Hawke's Bay team but it was still a step up from the previous week's loss to the defending champions.
"We've still got to work together more but three points on a day with this much travel involved ... we've got to be happy."
Tasman United had a really good crowd behind them. They were very hospitable and this created a good atmosphere," he added.
For Hawke's Bay United's English striker Sam Mason-Smith it was a memorable homecoming as he played for Nelson club Richmond United when he first arrived in New Zealand.
Auckland City and neighbours Eastern Suburbs maintained their lead in the Premiership yesterday. Auckland City beat Southern United 1-0 at Invercargill's Rugby Park Stadium while Eastern Suburbs pipped Waitakere United 1-0 in the first Premiership clash to be played at William Green Domain.
Other tussles saw Canterbury United beat Wellington Phoenix Under-20s 4-1 at English Park in Christchurch and Team Wellington beat Hamilton Wanderers 5-2 at Newtown Park.