Bowman was called up by the Hurricanes this week and played in only his 36th NHL game spread over three seasons. The goals were the second and third of his career.
After the Hurricanes fell behind 2-0 early in the second, Bowman started the comeback by scoring on a tip-in with 4:08 to go in the middle period. Tuomo Ruutu then scored on a slap shot with 52 seconds remaining to tie it.
Bowman put Carolina in front 37 seconds into the third and Jaroslav Spacek produced a power-play goal 6 minutes later.
Carolina won for just the 10th time in 33 games this season, ending a two-game losing streak.
Vancouver has lost two in a row after winning four straight. Cory Schneider made 37 saves for the Canucks.