Bryan’s own goal, which was originally credited to Roberto Firmino, was Liverpool’s 7,000th goal in top-flight football and secured a win which moves Jurgen Klopp’s champions within two points of fourth-placed West Ham.
Sadio Mane had an effort ruled out for offside before McBurnie squandered a glorious chance to equalise, the unmarked Scotland striker heading Norwood’s cross wide from eight yards out.
It was to prove a costly miss as Liverpool doubled their advantage after 65 minutes.
Firmino played one-twos with Jones and Mane and evaded a posse of home defenders to find a shooting angle and give Liverpool breathing space.
But television replays showed the ball was going wide before deflecting off Bryan, denying Firmino his seventh goal of the season.