The Cherries, who were mid-table until picking up eight wins from their last 10 games, raced into a 2-0 lead within 20 minutes thanks to two goals from livewire winger Matt Ritchie before Yann Kermorgant's diving header saw off the Royals before the break.
Their eye-catching victory, which saw silky one-touch football coupled with a high pressing game, was their fifth in succession and left a sold-out Dean Court dreaming of the most unlikely of play-off spots.
"I can believe we are here as I've seen how hard the lads have worked," Howe said.
"We didn't expect it but why not seize the moment and see where we can go?
"I know people will talk about the play-offs and I'm not stupid, I can see how many points we have and where we are in the league but it is in Reading's hands. If they win their five games, they are in it.
"We've always believed we have really good players and now we have the goals to justify me saying that.
"It was an incredibly hard-working performance and probably the quickest game we've played in this year.
"I was absolutely delighted with how hard our players worked. We pressed as well as we have this season and the lads are shattered in there."
While Harry Redknapp's post-match praise of 20-goal Lewis Grabban had the Cherries' number nine in the headlines, this week it was the display of his strike partner Kermorgant that had Howe purring.
He netted his sixth goal in 11 games since making the January move from Charlton and his hold-up work and clever play has allowed the pacey Grabban to thrive.
"It goes without saying that Yann has made the difference to the team," Howe said. "With him coming in the other lads have grown in confidence as well. Some of the interplay we have produced in recent weeks has been a joy to watch.
"No-one wants to play that pair at the moment. They are totally different and that is their strength. They both bring different things to the team, and it was great to see Yann score again."
For Reading, they welcome Leicester on Monday night looking to bounce back from this emphatic loss, their first on the road since January 25.
Having gone into the interval shell-shocked by Bournemouth's third they upped the ante in the second half and had Hal Robson-Kanu's stunning consolation to show for their efforts.
And Nigel Adkins, whose side have a two-point cushion over the chasing pack, was keen to remain upbeat.
"There is a hell of a long way to go," he said. "We have to keep the group together and keep positive.
"We've got to keep going because we are very much in this race.
"I'm very positive in my outlook and we have to show the spirit and desire to go for the next game.
"Give Bournemouth all the credit, we are not looking to make any excuses. They were very good on the night, especially in the first half and took their goals well."