Tavernier made his 24th Premier League start of the season at Kenilworth Road, and he went close to finding the net in the first half when he rattled the frame of the goal.
The 25-year-old would ultimately go on to score the opening goal in the 52nd minute, picking out the bottom corner with a driven strike from the edge of the box.
Unfortunately for Tavernier, it proved to be one of his final acts before he was forced off just shy of the hour mark.
In Tavernier's absence, the Cherries were unable to withstand a late fightback by their relegation-threatened opponents.
Jordan Clark restored parity in the 73rd minute, before Carlton Morris completed the turnaround in the final minute of regulation time.
Following the disappointing result, Bournemouth boss Andoni Iraola revealed that Tavernier will have to undergo a scan after suffering a hamstring issue.
"It's a hamstring injury," Iraola told the Daily Echo. "It is going to be difficult, I hope he plays before the end of the season, but we have to see the MRI and what it tells us.
"I think he had a very good week. Today he had good chances in the first half. In the second half he scored and was defensively doing really well.
"But these things happen and probably in the worst moment for him and for us, in this moment of the game. But it is a hamstring injury and it is going to be difficult."
Adams suffers another injury setback
Iraola also confirmed that Tyler Adams was left out of the squad due to a back problem rather than a recurrence of his hamstring injury.
"Tyler woke up two days ago with back spasms, and he wasn't available," Iraola added. "It is nothing related to the hamstring, but he was not available for the game."
Adams, who completed a move from Leeds United last summer, has seen his first season with the Cherries disrupted by injury issues.
The USA international returned from a long absence to appear as a substitute in last month's reverse fixture against Luton, before he made his first Premier League start for the Cherries in a 2-1 win over Everton.
Bournemouth will have to pick themselves up from their first defeat since February when they play host to Manchester United next weekend.