Alex Mowatt opened the scoring with a drilled bottom corner strike following a scramble inside the penalty area.
The Cherries created very little and have a tough run of fixtures heading into the back end of this EFL Championship.
Fluctuating form the frustration for Albion
Although it proved to be a promising night for Steve Bruce's side, it was marred with frustration that if they were to produce performances like these more often things may be very different for them.
Their victory over Fulham in their last home game set the standard for the games that were to precede them.
However, the showings that followed against Bristol City and Birmingham City were poles apart from the win over the division's runaway leaders.
Many Albion fans have continued to be perplexed by the players' dramatic swings in form and application.
When the pressure has been on to provide a performance in order to bolster their league position, they've faltered.
But when all hope of a play-off place has disapparated, a top-drawer showing is pulled out of the bag.
Perhaps this has been an issue with mentality, but Bruce must wrangle this side together as he fights to stay another term as Baggies boss.
Cherries glancing over their shoulders
Although looking nailed on for a promotion spot through the majority of the season, Scott Parker's side must be starting to keep one eye on the league table.
Even though their form wasn't particularly poor before last night, fans have continued to voice their frustrations over the boss' conservative nature.
The two early goals really let the air out of what started as an intense and committed opening from the Cherries.
But they'll be feeling that those behind them could catch them, only being six points above Huddersfield Town in third place - albeit with two games in hand.
Sides such as Nottingham Forest look unstoppable at this moment in time and will take some halting, but finishing in the top two is certainly in Parker's hands.
Carroll sets example
And the striker has set the standard for others to follow after an impressive first few months in an Albion shirt.
His battling spirit and tackle-hungry attitude put the forward performance on Sunday to shame and made the difference in a tough game against the Cherries.
It's been clear to see that the attitude (whether good or bad) is infectious in the Albion camp, with some games indicating a togetherness but others highlighting a lack of mental strength.
Carroll goes a long way to rectifying that, he has instilled standards and benchmarks for his teammates to follow.
He took his goal very well and set down another reminder to the hierarchy at the club that he's earnt another year to be added to his current six-month deal.