Former United striker Solskjaer had just two days to prepare his players for his first match as caretaker manager.
Marcus Rashford opened the scoring in the third minute and a goal from Ander Herrera just before the half-hour gave them a 2-0 lead.
Cardiff pulled a goal back through a Victor Camarasa penalty in the 38th minute but Anthony Martial restored the two-goal margin minutes later and two goals from Jesse Lingard in the second half added gloss to the scoreline.
United scored five goals in a Premier League game for the first time since Alex Ferguson's final game in May 2013.
"Football is easy if you've got good players," the Norwegian interim manager told BT Sport. "They are a great bunch of players and their quality is unbelievable.
"I arrived on Wednesday night and only had Thursday and Friday with the players. Wayne Rooney texted me and gave me some advice -- so it must be down to him. He told me to make them play football, enjoy themselves and be Manchester United."
Solskjaer said he had worked on patterns of play and focused on getting full-backs Ashley Young and Luke Shaw to push on higher up the pitch.
"Your workrate is the easiest thing to work on," he said. "It is free. It is the attitude and application of the boys.
"If we approach all the games like this -- and we want them to approach them all like this -- with combination play and playing the ball forward then I'll be happy.
"The foundation was in the defending today. I thought the two centre-backs and two full-backs were brilliant today."
He said he was not daunted by the eight-point gap between United and the top four.
"I was proud and humble at the reception from the fans, it has been emotional all week," he said. "But it's a start and we move on."
Goalscorer Lingard said United played with "energy, enjoyment and excitement".
"When you've got confidence, you put yourselves in positions to score goals," he said. "That's what we did.
"We were playing higher and the full-backs were higher. We pinned them back and created a lot of chances."