Grabban, 25, scored either side of Yann Kermorgant'S acrobatic volley to fire the Cherries to their first win in the second tier of English football since Harry Redknapp's side of 1990.
With last season's star striker Brett Pitman still nursing a knock, ex-Millwall forward Grabban partnered Wes Thomas in attack and opened the scoring with a header on 26 minutes before rifling in the winner from 25 yards in the 66th minute.
Promotion-winning boss Howe said: "I am really pleased for him. Every striker needs to score and he took his goals really well.
"He maybe didn't grab the headlines last year but he was a key part of the team. He has always performed well even when he perhaps didn't score the goals.
"He scored two strange goals for him today - they are not his trademark, a header and long-range shot but I thought him and Wes were a real threat.
"I am happy with Brett, Lewis and Wes but really that is all we have for recognised strikers and to just have the three is not enough.
"We are looking but won't be rushed and panic while these boys are fit. They deserve their chance and they will get it.
"It was an important game for us as we knew we needed to start well. We scored two goals and were somewhere near our best today but we are going to need to do it every week."
Kermorgant's scissor-kicked equaliser straight after half-time got Chris Powell's side back in the game for the first time but any hope of picking up a point were dashed when Bradley Pritchard saw red for a two-footed lunge on Ryan Fraser after 84 minutes.
Disappointed Addicks boss Powell said: "I have not seen the decision again, but from first reactions it looks a dangerous tackle so there are no complaints from me and sadly he'll have to serve the ban.
"It was a superb equalising goal from Yann but we were beaten by a magic strike on the day and are disappointed to lose.
"Yann is a key player for us, he's a top centre forward and it's a marvellous way for him to start the season.
"When we had the momentum we should have kept our foot on the pedal and that's something we've got to learn and learn quickly.
"We have earned the right to be here, we certainly did last year but it is now about us cementing our position in the championship and see where it takes us."