The Togo striker, on loan from Manchester City, received a pass from fellow Spurs debutant Scott Parker in the 67th minute to round Wolves keeper Wayne Hennessey and slot home the opening goal, delighting Redknapp.
The Tottenham boss says it doesn't matter that Adebayor is a former Arsenal player as he has the freedom to do as he wishes and if that means playing well for their North London rivals, then so be it.
"Ade has got off to a good start so it is fantastic for him," Redknapp said.
"He has got to sustain that now and he can become a big hero at Tottenham.
"Listen, Patrick Vieira wanted to come to Tottenham two years ago. I met Patrick, went around his house, had a cup of tea.
"If Patrick wants to come to Tottenham, anyone can come to Tottenham who has played for Arsenal because you are talking about Tony Adams, Dennis Bergkamp, Vieira, the great legends.
"He was willing to come. Listen, they are professional footballers, not murderers. Why can't Ade go and play for another team."
And Redknapp also praised the performance of Parker who joined from West Ham United on transfer deadline day.
"Scott will be great for us not only as a player, but as a person, around the club. He is old school," he said.
"He is the sort of footballer that every club used to have three or four in their team. They don't breed them anymore.
"We needed someone like that and that is why we pushed for him."