Smith fired beyond Boaz Myhill from range with his left foot seven minutes into the second half after avoiding serious injury when he was the subject of a horror challenge from Baggies winger James McClean who received a straight red card in the 34th minute.
Albion managed to claw their way back into proceedings when defender Gareth McAuley glanced home Craig Gardner's corner on 79 minutes before Bournemouth edged ahead in the 87th minute through Daniels, who emphatically buried his penalty after Dan Gosling had been felled in the area by Darren Fletcher.
To make matters worse for West Brom, Salomon Rondon as their second player sent off after clashing with Gosling in an off-the-ball incident as Tony Pulis' men saw their winless run extend to four matches.
The victory saw Bournemouth move up to 14th on the Premier League table where they sit on 19 points, just one behind the 13th-placed Baggies.
- Bournemouth finding some form and looking like they truly belong int the top flight. Is manager Howe destined for great things?
- West Brom are on a bad run and need to find a win soon before they finds themselves embroiled in a relegation battle.
1st of many I hope! Great win today against a tough side. @AdamSmith912 with another goal pic.twitter.com/JetNeHIFH5
— charlie daniels (@chazdaniels13) December 19, 2015
Another massive win for us today. Nice work @chazdaniels13 & @AdamSmith912 fullbacks stepping up #AFCB#Cherries#TrainBuddy
— Glenn Murray (@GM_83) December 19, 2015
Gareth McAuley admitted Albion should've held out for a point against #afcb on Saturday https://t.co/MnWhQGUm1s#WBApic.twitter.com/TYC32jIDAN
— West Bromwich Albion (@WBAFCofficial) December 20, 2015
Bournemouth boss Howe on the importance of that result at West Brom:
"Whenever you come here, to get three points, under the conditions you are faced with, it is a huge three points and take nothing away from the lads.
"The fact it was against 10 men doesn't really change their threat from set pieces. It is a great win for us."
West Brom's Pulis on the red cards to McClean and Rondon:
"It's a reckless challenge from McClean. The disappointing thing for me is that 10 seconds before that Smith goes over top and catches McClean on his ankle. McClean has not let that go, he has gone after him. You can't condone that.
"Rondon can't do things like that. He's never had any inkling he's got something like that in him since he's joined us. That's the first time we've seen him react like that."
Goals - James Morrison, Salomon Rondon, Saido Berahino 3
Assists - Chris Brunt 4
Clean sheets - Boaz Myhill 6
Yellow cards - Chris Brunt, Claudio Yacob 5
Red cards - Gareth McAuley, James McClean, Salomon Rondon 1