The Dutch striker scored a goal in each half, making Bruce Anderson's late effort a consolation for the visitors.
With speculation mounting over the future of Tony Watt, who was left on the bench, Lucketti was pleased with Van Veen's contribution.
He said: "Kevin was terrific. It was a real centre-forward's display and his two goals were different class.
"He's a real matchwinner and the free-kick he put in the top corner was special, but he's capable of that. He was probably unlucky not to get another one from a similar position in the second half.
"Kevin also scored with a great header from Connor Shields' superb cross, so you can see why the fans love him.
"He can go from strength to strength because he's getting the rewards for his exceptionally hard work on the training pitch and we're also reaping the benefits of that."
Watt has made clear that he will not sign an extension to his Motherwell contract that expires in the summer.
He has been linked with a move to Dundee United and Lucketti admitted there was a chance the former Celtic striker could even leave next month.
He added: "There is a likelihood that he could leave in January but there's nothing set in stone yet so we'll just keep working away until we hear differently.
"We spoke to Tony and his state of mind was fine. We then picked a team to win the game.
"It's hard to say whether any money we may get for him would be used to help strengthen the team, but we will be ready to move if that does happen."
He said: "We got into really good offensive areas in the first half but we never tested the keeper. We never got crosses or balls into the box or any shots off.
"On reflection we probably dominated more possession but that doesn't win you games of football. Their number nine was the difference, Van Veen was the difference in the game."