Both Van de Beek and Cavani played the full 90 minutes at Old Trafford with an early brace from Bruno Fernandes followed up a penalty from Marcus Rashford and a late Daniel James strike.
Van de Beek was a reliable distributer in midfield, while Cavani worked tirelessly in the final third as the Red Devils claimed a third straight victory in all competitions.
Solskjaer was asked about his two summer signings after the match and stressed his belief that both are making promising progress in their adaption to the side.
"The two are getting used to how we want them to play - Donny can play in different positions and Edinson is a good old fashioned number nine and we haven't had that for a while and I was happy with how Anthony [Martial] played off the left," Solskjaer told BT Sport.
"I felt first half we saw the intent straight away, they wanted to play and they enjoyed it. It's a Champions League night at Old Trafford, you'd expect them to enjoy themselves. We scored some very nice goals, I'm pleased.
"We need one point, but of course we want to be top of the group but we'll take it one game at a time."
Despite being on a hat-trick, Fernandes allowed Rashford to take United's penalty in the 35th minute after the England attacker had won the foul.
Solskjaer had no issue with Fernandes delegating the spot-kick and is simply thankful to have a number of players willing to step up to the spot.
"Marcus is a very good penalty taker and Bruno is very confident, if Bruno wants to give it to Marcus then why not?" Solskjaer said. "Anthony Martial took one against Leipzig too - why not share it around?"
Next up for the Red Devils is a trip to St Mary's to face Southampton, with Ralph Hasenhuttl's side currently on a seven-game unbeaten run that sees them sitting in fifth place in the Premier League table.