The growing pressure on West Brom boss Gary Megson was eased after his side earned their first win of the season.
Kanu and Zolten Gera scored the goals in the second half after Darren Moore had a header cleared off the line by Gary Speed before the interval.
Kanu diverted in a Gera cross before the goal provider got on the scoresheet himself with a powerful header.
A Stelios Giannakopoulos free-kick pulled one back for Bolton but the Baggies held on for a vital win.
The match had started with a tense atmosphere at the Hawthorns which spilled down from the stands onto the pitch as the Baggies started nervously.
But Megson's players quickly shrugged off their early nerves and created several chances during a flurry of action.
It started with a long-range Gera shot going just wide before Geoff Horsfield was put through on goal by Kanu only to strike an instant effort tamely when he had more time and space at his disposal.
A Gera shot was then deflected out for a corner from which Moore's header was cleared off the Bolton goal-line as the home side increased the pressure they were exerting on the visitors' goal.
But the final touch in front of goal was deserting West Brom and it was no different when Jonathan Greening chested a ball before volleying over from just inside the area.
Bolton almost snatched an unlikely lead when Ricardo Gardner produced a mazy run and angled shot which keeper Russell Hoult spilled.
Kevin Nolan tried to squeeze the ball home from the rebound but hit the post.
A lacklustre Bolton suffered a setback when playmaker Jay-Jay Okocha had to go off through injury as they struggled to stamp any authority on the match.
Gera was a constant threat for the Baggies and he cut inside from the left flank to provide the cross for Kanu from which he slotted in from close range.
Gera's was then rewarded for a lively performance when he stole in at the near post to head home a corner.
But West Brom had to survive a late Bolton rally after an inswinging Giannakopoulos free-kick from the left flank was allowed to find its way into keeper Russell Hoult's net.
West Brom: Hoult, Haas, Gaardsoe, Moore, Albrechtsen (Dyer 81), Gera, Scimeca, Johnson, Greening, Horsfield, Kanu. Subs Not Used: Kuszczak, Contra, O'Connor, Earnshaw.
Goals: Kanu 57, Gera 65.
Bolton: Jaaskelainen, Ben Haim, N'Gotty, Jaidi, Gardner, Campo (Kaku 65), Speed, Okocha (Diouf 34), Nolan, Ferdinand, Pedersen (Giannakopoulos 58).
Subs Not Used: Barness, Oakes.
Goals: Giannakopoulos 73.
Ref: M Clattenburg (Co Durham)