The Reds' £45 million summer signing broke the deadlock just after half-time with a fine long-range finish at Villa Park, before Alysson levelled for the hosts and substitute Igor Jesus struck a late winner to seal Oliver Glasner's first victory as Nottingham Forest boss.
It was Delap's first goal since January, when he scored for Chelsea in a 2-1 defeat to Fulham during a difficult debut season at Stamford Bridge that yielded just one Premier League goal in 28 appearances.
Speaking to BBC Sport after the match, Delap said he is relishing the prospect of regular football since his move north.
"It's always nice to score, especially finishes like that," Delap said. "We know Villa play a really high line. I have only been here a few weeks but everyone has welcomed me and I have really enjoyed it.
"As a young player, all you want to do is play. I think I made a great decision to come here and hopefully I can play well.
"The manager has a very clear plan of how he wants to play. Today, we showed we can execute it."
Forest had tracked Delap during the summer of 2025 following his impressive season at Ipswich Town, only for Chelsea to win the race for his signature at the time. Twelve months on, the 23-year-old has now made the switch to the City Ground.
Former Brentford manager Thomas Frank was among those impressed by his display, telling Match of the Day the move looks a shrewd piece of business.
"I think he is a very good signing for Nottingham Forest. And I think Glasner has played a big role in wanting him in," Frank said. "The goal is excellent. It is a brilliant strike - and that is one of the more difficult ones to score.
"In general, I really like Delap. I think with more confidence, more game time and if he stays injury free for the season, I am very confident he will score a lot of goals - like 12 to 15."