Grabban scored three times in 18 second-half minutes, the third one from a rebound after Dean Bouzanis had saved Harry Arter's penalty, following a goalless first half in which there was little incident at either end.
Charlie Daniel scored Bournemouth's fourth with an 81st-minute header before Matt Smith got an 86th-minute consolation in a rare Oldham attack.
Howe said: "Lewis has everything to be a top-class striker. He worked well with Lee Barnard and he deserved his goals."
Howe added: "The lads were excellent in the second half. It's always good to get the first goal and we were mindful that Oldham had lost their last two.
"The good run continues, but we have a lot catching-up to do. We are keeping the momentum going and I'm happy we are still under the radar."