Brannagan produced a cool finish with 17 minutes to go at Prenton Park after latching on to a pass from Sheyi Ojo, who continued his return to fitness by playing the full 90 minutes.
We're not quite sure how that ended level... pic.twitter.com/vMmoSJzypY— Liverpool FC (@LFC) December 6, 2016
See: Liverpool report
West Brom, who had taken the lead through Andre Wright's looping header in the first half, remain second in Group G, three points behind the Merseysiders, with four points from three matches.
The match was the last in charge for Liverpool's Premier League 2 manager Michael Beale, who has left the club.