Having fallen behind to Petar Stanic’s first-half strike, Kudus forced the visitors into an own to level the score after the restart.
The 23-year-old then put West Ham ahead with a fine header after connecting to a cross from James Ward-Prowse.
Tomas Soucek then added a third goal late on as David Moyes’ side completed the turnaround to seal victory at home.
Reacting to his debut strike in the aftermath of the match, Kudus said it means a lot to be up and running among the goals.
“On the first goal, I don’t know if it’s mine but the ball touched me a little bit, then I just turned and the ball was in the goal,” he said.
“I just had to be there at the back post. I spoke with Saïd at the start of the game and I told him any time he cuts in I would be at the back post – and I was there!”
“We know James Ward-Prowse has a fantastic delivery and any time we have a set-piece we have a chance to score. On that one I just took my responsibility, made the run and it went in.”
Kudus joined the Premier League side from Ajax Amsterdam in August after putting pen to paper on a five-year contract.
The young playmaker made his debut as a substitute in the Hammers’ 2-1 Premier League win against Luton Town before the September international break.
Kudus again came off the bench in their 3-1 defeat at the hands of Manchester City last Saturday and, after starring in the Europa League, it’s likely he’ll start against Liverpool at the weekend.