United trailed the hosts 2-0 at half-time but managed to claw their way back to seal the three points.
Cavani, who replaced Mason Greenwood at the break, was involved in every goal, first by passing to midfielder Bruno Fernandes to pull one back just before the hour mark.
The Uruguayan hitman followed up with a goal of his own 15 minutes later and then heaped misery on the hosts when he struck in stoppage time to seal an eighth consecutive away victory in the Premier League.
Cavani now has three goals from five substitute appearances in the league for United since he joined in a free transfer and Solskjaer has been impressed by him so far.
"Great impact of course. He is a number nine who wants to be in between the posts, he is always on the move, he wants to get in front of you and I am very pleased with him," he told BBC Sport . "On the training pitch, in the dressing room and during meal times, how meticulous he is. He knows what he wants to eat, how much he wants to recover - everything!
"It was top movement and his timing is fantastic. His hunger to get on the end of things is the key for a centre-forward. Sometimes it hurts and sometimes it doesn't but to score you have to be in there."
United captain Harry Maguire hailed the 33-year-old forward as the best he has ever faced in training and expects great things from Cavani at Old Trafford.
"His movement is excellent in the box. He's the best I've played against during training. He is on the move constantly," he said. "We know what he has got and can bring to this club. It's important he kicks on now because he's a top, top player."