The 21-year-old converted Ahmed El Mohamady's cross in the eighth minute to help the Villains end their four games winless run.
The win was Dean Smith's first after succeeding Steve Bruce at the helms of the West Midlands outfit earlier this month.
Ghana's Albert Adomah, Cote d'Ivoire's Jonathan Kodjia and DR Congo's Yannick Bolasie were also in action for hosts.
Abraham who is on a season-long loan from Chelsea has now scored four goals in seven league games for the Villa Park outfit this term.
Aston Villa moved to the 13th spot in the Championship log with 18 points from 13 games. They visit Norwich City for Tuesday's league meeting.