The clash was Everton boss David Moyes' first visit to the Stadium of Light since he oversaw the Wearsiders' relegation from the Premier League in 2017 and his current side took the lead when Iliman Ndiaye struck after 15 minutes with his fourth league goal of the campaign.
However, the hosts levelled seconds after the break as Xhaka's effort bounced off James Tarkowski's foot and into the net for his first goal for the club.
Monday night's draw lifted Sunderland up to fourth in the table and left 14th-placed Everton without a win in their last three games.
Former Black Cats goalkeeper Jordan Pickford received a warm reception as he came up against his boyhood club for the first time since moving to Merseyside in 2017.
He nearly helped the Toffees go in front seconds into the game, booting a long ball up field which James Garner fired wide.
Following a quick move down the left, Kiernan Dewsbury-Hall played a neat pass into Ndiaye, who had his shot blocked before Barry had an effort smothered as Everton enjoyed a lively start.
Ndiaye soon put them ahead. Barry challenged Noah Sadiki and, with no foul awarded, the attacker quickly took advantage, racing away and weaving through the home defence to curl a shot past Robin Roefs from the edge of the area.
An unsettled period followed for the hosts with Jack Grealish's strike coming back off a post.
The Manchester City loanee was in the thick of the action again, sending a deep cross into Barry at the back post, but the forward blasted over the bar from inside the six-yard box.
Sunderland finally began to show some attacking intent, with Lutsharel Geertruida sending a dipping effort over and Enzo Le Fee's curling delivery punched away by Pickford.
The home side picked up where they left off after the restart, levelling 43 seconds into the second half when Le Fee played a neat ball into Xhaka and the skipper's powerful effort deflected off Tarkowski's foot and into the roof of the net.
The game evolved into a scrappy contest, with both sides struggling to really test either keeper until Wilson Isidor latched on to a loose ball in the 71st minute and charged towards goal, blasting over the bar.
Nordi Mukiele nodded over from Xhaka's delivery and, as the game entered the final 10 minutes, Roefs made a stop at his near post before holding Grealish's teasing cross.
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