Since Solskjaer replaced Jose Mourinho at the helm for United, Lukaku has had to contend with playing second fiddle to Marcus Rashford or being shunted out wide.
With Rashford suffering a knock against Liverpool on Sunday, Solskjaer left him on the bench and started Lukaku as the focal point of the attack against Palace and the Belgian grasped his opportunity with both hands, scoring United's first two goals.
Ashley Young then wrapped things up late on after Joel Ward had pulled one back, but it was Lukaku who Solskjaer focused on after the game.
"Lukaku had two good goals and his link up play was very good too," Solskjaer said.
"He is working hard in training and has been playing well. He's had to play wide for me and had many defensive duties, so I'm happy for him playing as a number nine.
"It's always good to see players taking their chance. That's what it's about at this club, when you get your chance, grab it."
Injuries meant Scott McTominay got a second successive league start and was quietly impressive, while Fred was named in a top-flight starting line-up for the first time since Boxing Day.
Solskjaer also handed a debut to 17-year-old midfielder James Garner towards the end, and the Norwegian was glad to give opportunities to those lacking them in recent times.
"It's a great away win. We controlled it well," Solskjaer added. "That's a few away wins on the bounce.
"Fred and Scott McTominay haven't played much and we got another debut for one of the kids coming through too in James Garner.
"He is in the mould of a top, top central midfielder, so he will come good. We will see him again soon.
"It's Manchester United, we do have a quality squad and quality players, and we will continue to bring players through."
Despite a brief period on top when Palace scored, manager Roy Hodgson felt United were deserved winners, though he does not think his team should be too hard on themselves.
"We were comfortably beaten in the end," Hodgson accepted. "I give the players credit because they didn't fold at 2-0 down and we played quite well.
"At 2-1 we were having a go and had high hopes, but we were caught on the counter. We weren't good enough to take anything from the game, there's no point worrying about ifs and buts. Everyone has ifs and buts."