Wanganui got the 5m scrum and spread to the far corner where hooker Jack Yarrell drove his way over, with Tavae adding the sideline conversion.
However, some poor kicks put the home side under unnecessary pressure in the shadow of halftime, and after receiving a penalty, Hawkes Bay tapped and forced their way under the posts to close the gap to 14-12.
Taking the breeze, Wanganui kept play in their attacking half of the field, but struggled to convert pressure into points with some handling errors and hard Hawkes Bay tackling, especially around the hour mark as they were still putting in some jarring hits.
Nonetheless, the gaps finally opened as Tavae was dragged down near the line, then reserve front rower Isaac Greer came charging from a long way back to nearly crash over, with the ball recycled for winger Josaia Bogileka to go over beside the ruck.
Wanganui then held out for the last 15 minutes to finish their run of Under 19 matches with wins over Manawatu and Hawkes Bay, along with the loss to Taranaki.
Halfback Rory Gudsell, lock Jack Hodges and No8 Kieran Hussey were standouts.
Coach Ross Williams is likely to get a couple of extra players to join his side with Steelform Wanganui coach Jason Caskey firming up who will be his final squad to start the Mitre 10 Heartland Championship on August 27.