The supporters inside the Vitality Stadium were treated to an entertaining first period, which kickstarted with Antoine Semenyo's opener.
With the scores level at the break, Solanke moved his side back in front in the 52nd minute, stroking the ball home after being teed up by Milos Kerkez.
Despite falling behind for a second time, Aston Villa still left the South coast with a point after Watkins produced a clinical header to extend his side's unbeaten run to five competitive matches.
While the visitors remain in fifth position, Bournemouth will finish the weekend in 14th place and six points clear of the drop zone.
After winning their previous two matches, a confident Bournemouth side made a positive start to proceedings, taking the lead in the 10th minute through Semenyo.
Ryan Christie won possession high up the pitch before feeding the Ghana international, who drove a low strike into the bottom corner.
Unfortunately for the Cherries, their slender lead lasted just 10 minutes until Bailey restored parity with his fourth league goal of the season.
The winger was given the time and space to drift into the box onto his favoured left foot, before he drilled the ball into the far corner.
With momentum in their favour, the Villans thought they had completed a quick turnaround when defender Diego Carlos slotted past Neto, but to the visitors' dismay, the goal was chalked off for an offside infringement.
As the contest moved past the half-hour mark, Solanke was denied at point-blank range by the sprawling Emiliano Martinez.
It was then the turn of Martinez's opposite number to make a fine stop, as Neto stood firm to keep Douglas Luiz at bay.
After going into the break on level terms, the Cherries flew out of the gate in the second period to restore their advantage within seven minutes of the restart.
The marauding Kerkez picked out Solanke, who quickly swivelled and fired into the bottom corner to register his seventh league goal of the campaign.
Solanke was then presented with a chance to double Bournemouth's advantage, but like the first half, the striker was thwarted by the resilient Martinez.
The Argentine's superb save proved to be a crucial one, as Watkins pulled his side level in the 90th minute, arching his neck to reach Moussa Diaby's lofted cross and guide his header past the helpless Neto.
Aston Villa will now turn their attention to a difficult midweek clash with the champions Manchester City, while Bournemouth will face Crystal Palace at Selhurst Park.No Data Analysis info