The Black Cats needed extra-time goals in the third round replay from Julio Arca and substitute Michael Proctor to break down a stubborn Bolton.
Both managers made eight changes to their respective sides held to goalless home draws at the weekend to emphasise just where their priorities lie.
Sunderland boss Howard Wilkinson included Arca for the first time this season and handed debuts to Sean Thornton and £3.5million signing Nicolas Medina.
But former Blackpool youngster Thornton completely overshadowed the Argentina Under-20 international with an impressive performance in midfield.
"Sean looked very comfortable and I think there was a lot of plusses out there tonight,'' said Wilkinson. "I thought we got the result we deserved, the performance was good and we played without fear.''Bolton boss Sam Allardyce offered no excuses, and faced with an extra Premiership match with Newcastle this month, welcomes the free weekend when the fourth round ties are played.
"We should have won the first game at our place and we should have beaten Fulham last Saturday, but we were second best tonight,'' he said. "Kevin Poole kept us in it but we were found wanting in certain areas.
"We were not very good and could not cope with all the changes or the conditions. But I'm disappointed we are out of the Cup.''Sunderland should have had the tie wrapped up in normal time with Kevin Kyle guilty of squandering the best of the chances. He failed to hit the target with two close-range headers and when he did manage to test Poole, the keeper was equal to the challenge.
Thomas Sorensen denied Youri Djorkaeff from converting Bolton's best chance but Sunderland finished strongly with Marcus Stewart, Kyle and Gavin McCann all going close.
But they finally found a way through in the 98th minute when Arca drilled a low drive past Poole and in the next minute Proctor scored a delightful goal when set up by Darren Williams.