The 21-year-old helped set up the first goal, winning a duel against Cristian Romero to flick Jens Cajuste's cross towards Sammie Szmodics, who opened the scoring with an overhead kick.
He then got on the scoresheet by capping off an impressive team move, rifling the ball into the roof of the net to make it 2-0 before the half-time interval.
Delap battled hard throughout his 70 minutes on the pitch, catching Shearer's eye as a result.
"Got a goal and an assist and also held the ball up brilliantly to relieve pressure, often against two centre-backs," he wrote. "A complete centre-forward's performance."
Shearer also named Town boss Kieran McKenna as his Manager of the Week, saying: "What a way to get your first win of the season! His side showed real quality to go two goals up, and then great determination at 2-1 to deny Spurs an equaliser."