"You can't take it away from two of their guys," said Wanganui coach Stuart Gillespie. "We should have won but we didn't."
Kinnerley would finish with 6-65 as part of a nine-wicket haul from the match.
After bowling a long spell, he took a short rest before returning to try and prise Fowler and Kennett out of their crease, but the pair held firm.
Gillespie said allrounder Nick Harding deserved better from his 16 overs, having created chances, including getting Fowler to fall into a trap; however, the ball was dropped at the boundary.
Gillespie said the team was very tired at the close of play, coming from 50 over cricket to spending over 10 hours at the ground, if you include the rain delay.
So, while Wanganui missed three more competition points for outright victory, they can take a lot of confidence from the seven they banked for the first innings, with their first innings total being easily the biggest of all three Hawke Cup games played at the weekend.
Key was wicket-keeper Chris Sharrock's inspiring 104 not out, striking 15 boundaries, in a case where, unlike some of the top order, his concentration matched his timing and confidence.
Gillespie said it was that confidence the team had to take into the New Year and their next match - a tough ask against Manawatu in Palmerston North on January 16-17.
Gillespie said the team was disappointed not to finish it off, but they have a self-belief that they can play.