Steve Bruce's side registered their second consecutive stalemate in the Championship days a similar outcome against Bristol City.
Kodjia gave the hosts a promising start at the Villa Park with his 26th-minute opener followed by Abraham's effort that doubled the lead eight minutes before half-time.
After the restart, Preston North End staged a dramatic comeback and took the lead in the 86th minute but substitute Bolasie who replaced Kodjia in the 74th minute, was able to rescue a point for his team.
FT: #AVFC 3-3 #PNEFC— Aston Villa FC (@AVFCOfficial) October 2, 2018
Crazy game. Gutting finish as Glenn Whelan has a penalty saved to deny us a winner. That after @YannickBolasie equalised late on, following a Preston turnaround. In the end, we take a point.#PartOfThePride pic.twitter.com/PJdn6pHO3C
Glenn Whelan misplaced a last-gasp penalty that could have handed the Villans their fourth league win of the season.
Aston Villa climbed to the 12th spot in the Championship log with 15 points from 11 games. They visit Millwall for their next game on Saturday.