Pavlyuchenko was on target in the 2-1 victory against Everton on Sunday to move Spurs back into the top four of the Barclays Premier League - but Tom Huddlestone was carried off on a stretcher and added his name to growing list of players in the treatment room.
"He's got a future here while he's playing well and scoring goals," said Redknapp of the former Spartak Moscow striker.
"We had a Russian club wanting to buy him and a Premier League club wanted to buy him but I spoke to the chairman and said I want to keep him.
"He scores goals, that's five goals in two-and-a-quarter games and you can't ask more than that. It's good, it gives me a nice problem, I've got good front men.
"He's had the opportunity, he's taken it and he's got to keep taking it and keep playing like that. It's up to him."
The visitors should have earned a point but Landon Donovan missed an open goal.
"Landon is disappointed," Moyes said. "It happens in football."
Moyes revealed that Louis Saha was missing from the matchday squad through injury.
"He has a bit of a hamstring and a bit of an Achilles," he said. "We've not had the scan read yet."
Source: PA
Source: PA