Connell scored twice and had a hand in Sammy Igoe's goal as Cherries struck back from 1-0 down to emphatically see off the challenge of League Two rivals Chesterfield on Saturday.
The former Hereford and Brentford hotshot produced another improved display to help Cherries record a highly-impressive 3-1 win, inflicting the Spireites' first defeat on home soil this season in the process.
And Connell's joy was in stark contrast to the disappointment he suffered following a penalty miss as Cherries lost at the Derbyshire venue back in February.
Discussing that spot-kick, the popular 26-year-old told the Echo: The boys were winding me up a little bit before the game, saying I hope we don't get a penalty today Al' and all that sort of thing.
But I was delighted to exorcise that ghost, because it was a difficult time last season and that was a bad memory.
It was great to score two and I wish I'd got another one, but I'm happy I scored two and we're through.
Connell, a fans' favourite during his first spell with Cherries between 2002 and 2005, has endured a tough time since returning to Dean Court.
He has suffered injury problems, which paled into insignificance when his late mother Sue passed away in March following illness.
The frontman netted his first goal since moving back to Dorset against Yeovil in September and his performances have steadily improved in recent weeks
Connell said: I'm really pleased with how the past few weeks have gone.
I feel fit and sharp and I'm enjoying playing for this team.
On another day, Connell could quite easily have claimed the match ball, having failed to work the goalkeeper with two second-half headers.
If I'd have missed those on a hat-trick I would've been more disappointed, he added.
But I was pleased to get in those areas and get good contact on them. I probably should have hit the target with at least one of them, but I'm really pleased with my form and the team at the moment.
We've got to be pleased we're in the next round and I think that will give the whole club a boost.
Boss Eddie Howe added: I felt this was a game suited to Alan and he didn't disappoint. I thought he was excellent.