The first half saw the hosts go down to ten men, as James McClean was dismissed for a late challenge on Adam Smith. The Cherries right back then dusted himself off in the second half and went down the other end to fire his side ahead.
West Bromwich Albion responded and Artur Boruc had to be on his toes to deny a fine strike from Salomon Rondon but he do little to prevent Gareth McAuley's header levelling proceedings moments after.
The Cherries were not done, however, and Dan Gosling was felled in the dying minutes of the match to win a penalty which Daniels then stepped up to convert.
Eddie Howe named an unchanged team for the visit to the Hawthorns, however an injury to Joshua King in the warm up eventually saw Glenn Murray become the one change in the line up.
The Cherries began brightly and a marauding run for Daniels saw the defender unleash an early effort at goal which deflected behind for a corner.
AFC Bournemouth seemed to find their rhythm after this and a free-flowing move earned a dangerous crossing position from right, yet Gosling's early cross was slightly askew.
The home side then took their first blow of the afternoon as McLean was given his marching orders for a late tackle on Smith.
Gosling soon made use of the man advantage and darted into the West Brom penalty area looking to tee up Junior Stanislas, but his cross fell just behind the in-form winger.
The Cherries were starting to create real chances now and Stanislas returned with a cross of his own, but Matt Ritchie’s back-post header flashed just wide in what was the final chance of the first half.
The hosts made one change during the interval to reshuffle their pack, as Stephane Sessegnon made way for James Morrison.
That change appeared to spark West Brom into action. Shortly after Rondon forced a sublime save from Boruc and the Poland international was then called into action again shortly after to punch clear the resulting corner.
Having weathered the early storm, AFC Bournemouth then took the lead through Smith. The right back received the ball on the left flank and cut inside past two defenders before unleashing a left footed drive into the bottom corner.
The Cherries looked good value for their lead and nearly doubled it shortly after. Ritchie struck a free kick from the same position as Smith’s effort, but the Scotland international’s attempt deflected just wide for a corner.
Moments later Stanislas picked up the ball on the left of the penalty area and rattled a strike against the post, before the winger was then replaced by Marc Pugh. Yann Kermorgant was also introduced shortly after in place of Murray.
Despite the pressure it was the home side that forced the next blow. A dangerous in-swinging corner flew towards the Cherries near post and was headed in by McAuley on the 80th minute to level proceedings.
Eddie Howe then responded with an attacking substitution, as Tokelo Rantie replaced Arter.
On the 86th minute Gosling picked up the ball on the halfway line and drove towards the West Brom penalty area before being pulled down by Darren Fletcher, leaving referee Mike Dean with little choice but to point to the spot.
Daniels stepped up confidently to dispatch the resulting spot kick in off the crossbar to restore the lead and send the Cherries fans behind the goal into raptures.
In the dying moments substitute Pugh had a chance to extend the lead further, but was denied by Boaz Myhill from close range.
West Brom: Myhill, Olsson, Evans, Morrison (Sessegnon, 45), Gardner, Brunt (Lambert, 74), McClean, McAuley, Fletcher (Berahino, 90), Dawson, Rondon
Not used: Lindegaard, Chester, Anichebe, McManaman
Booked: Evans, Fletcher
Sent off: McClean, Rondon
Goals: McAuley, 80
Cherries: Boruc, Francis, Cook, Gosling, Surman, Arter (Rantie, 82), Daniels, Smith, Stanislas (Pugh, 69), Murray (Kermorgant, 76), Ritchie
Not used: Federici, Distin, MacDonald, O’Kane
Goals: Smith, 52, Daniels, 86