Cherry pop for Solanke
from the left and the unmarked Billing volleyed into the net.
Solanke thought he had doubled Bournemouth’s lead but his header from a Ryan Fraser corner was chalked off after VAR spotted Harry Wilson had strayed offside.
Bournemouth continued to dominate possession but failed to produce much cutting edge.
The profligate Cherries should have been punished in stoppage time when Billing hauled down Matty Pearson in the area but Alan Sheehan fired the spot-kick against the bar.
England star Wilson was called off the bench in the 63rd minute and the move paid instant dividends.
Mark Travers played a long ball out from the back that allowed Harry Wilson to run at the defence.
He squared the ball to his namesake, who confidently converted into the corner. Billing made sure of the win with 11 minutes left with a deflected right-foot shot from 25 yards out.
The icing on the cake came three minutes later when Solanke belatedly opened his account.
Luton failed to deal with a routine ball in the box, which fell kindly for Solanke to smuggle in from 12 yards.
Solanke barely broke into a smile but Howe will be hoping the goal proves the turning point for the former England Under-21 star and the result a turning point for his side.
BOURNEMOUTH LUTON 6 ........ Shots on Target .......... 1 4 ........ Shots off Target ......... 5 4 .......... Blocked Shots ............ 1 12 ............... Corners .................. 1 8 .................. Fouls .................... 7 3 ............... Offsides .................. 1 64 ........ Possession % ........ 36 62 ...... 1st Half Poss % . ...... 38 64 ..... 2nd Half Poss % . ..... 36