In the 52nd minute, big second five Timoci Seruwalu scored against the team he has played for on loan for the previous two seasons, and then in the 67th minute Clare ran in for a brilliant 90m try.
Wanganui sealed it with Clare's double right on fulltime, with the conversion giving him a 21-point haul.
Coach Jason Caskey said early handling errors prevented the side from taking control until after the break.
"We had a very poor first half actually.
"It was the ball going away from you a bit, probably a bit guilty of snatching at it.
"After that, it was pretty much we had control of the game and defended well.
"We moved it around a bit, played our game. Our forwards got dominance at scrum time, the lineout was good too."
Young halfback Cameron Davies covered the first half, before Wanganui brought the veteran Lindsay Horrocks on for the second stanza, and he introduced some more urgency.
Hooker Joe Edwards and lock Josh Lane, who had been working through a sore ankle during the week, were the standout forwards, while Caskey praised Bogileka for a very good match with a high workrate – shifting to cover the wing after Vereniki Tikoisolomone came off sore from a knee to the back.
While Tikoisolomone should recover fine, prop Wiremu Cottrell suffered a corked thigh and may be doubtful for the next game against King Country.
Captain Campbell Hart agreed the team had put training into practice after their loss to Hawke's Bay Saracens by not doing such easy-to-read carries, even if the backs had to work for longer with less cover on the bench.
"We didn't want to go into our shell, we want to play our game and move the ball.
"We just take the ball a bit wider.
"It was basically hands let us down in the first half.
"Second half, we got into our rhythm, we didn't really let them get the ball."
The win with a bonus point sets up a decisive match with cup-holders Wairarapa Bush at Cooks Gardens on October 17, but next up are King Country in Taumarunui, as Wanganui defend the Sir Colin Meads Memorial Trophy.
Wanganui 36 (C Clare 2, D Whale, J Bogileka, T Seruwalu tries; Clare pen, 4 con) Horowhenua-Kapiti 7. HT: 10-0.
First class gamesOctober 10: v King Country, Taumarunui (Sir Colin Meads Memorial Trophy); October 17: v Wairarapa Bush, Whanganui (Bruce Steel Memorial Cup round-robin); October 24: v Poverty Bay, Napier (Curtain-raiser to Hawke's Bay v Manawatu).