Benik Afobe gave Bournemouth the lead, heading home firmly after 13 minutes, and Patrick van Aanholt equalised just before halftime, firing home a fierce shot from a tight angle to score for the fourth game in a row.
Lewis Grabban missed a great chance to win it for Bournemouth but Sunderland remained second-bottom of the standings, six points behind their opponents.
"After their goal went in, there were 20 minutes where we hung on, but we stopped them scoring, which we haven't done recently," Sunderland manager Sam Allardyce told the BBC.
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"We've gained a result from going a goal behind and that shows a bit of character from the players. They overcame their fears and came back strongly. It's a precious point."
Bournemouth manager Eddie Howe was left frustrated.
"We dominated the early stages, we were in total control. Today was a real number nine's goal from Benik Afobe and he was a real handful," Howe said.
"The pleasing thing is the resilience we showed in the second half. But today we were the dominant team and that's the disappointment."
(Reporting by Ed Osmond, editing by Ian Chadband)
