Goals from Lee Tomlin, Abraham, Aden Flint and David Cotterill helped Lee Johnson's men move out of the bottom four of the English Championship log.
The Anglo-Nigerian scored on the brink of half-time, after Tomlin had fired them into an early lead against third-place David Wagner's team.
In the 79th minute, Flint made it a 3-0 lead before Cotterill completed the rout.
It is the England youth international's first goal since returning from Chelsea - where he underwent treatment on a thigh injury in February.
The win means City move up to 19th on the English second division log with 41 points, two away from safety and level on points with 20th-placed Burton Albion.