The Baggies recovered from a goal down to pick up three more points in the West Midlands, seeing them tighten their hold on eighth place in the Premier League table.
Joshua King's early penalty gave the Cherries hope of ending their alarming run of three successive defeats, but Albion soon hit back through Craig Dawson and Gareth McAuley to make it four wins on the spin on their own patch.
The match turned on its head soon after, however, as Dawson's driven shot deflected beyond Boruc to level things up and McAuley found a way through from close range to put his side ahead.
Albion thought that they had breathing space when Chadli nodded in Chris Brunt's corner 50 minutes in, but referee Mark Clattenburg - with help from his officials - ruled it out following a clash of heads in the box.
Fresh from becoming a father for the first time, Harry Arter sent a shot narrowly wide of the upright, while King could only head over from a Smith cross.
Just when the chances looked to have dried up, Lys Mousset tested Foster with a stinging shot at the death and headed wide from the resulting corner.
There was still time for Tyrone Mings to also test Foster with effectively the final act of the contest, with the big stop from range ensuring that Albion have now lost just one of their last eight league outings overall.