The Welsh outfit claimed their second victory in four games since Solskjaer took charge, with the decisive moment coming in the 50th minute when Fraizer Campbell slotted in.
Both ex-United man Campbell and the man who supplied the cross, Craig Noone, had come off the bench, as they did in the third round at Newcastle where a goal from each subsequently secured a 2-1 triumph.
The match was watched from the stands at the Reebok Stadium by United manager David Moyes and did not provide much in the way of entertainment, with very few real goalscoring opportunities being created.
But Solskjaer was delighted with the way his team approached the task of seeing off their Sky Bet Championship hosts and thought it was a good way for Cardiff to warm up for their other north-west assignment.
Asked if it had been the perfect preparation for the Old Trafford encounter, the Norwegian said: "Definitely. For players to get confidence and to feel good, you have to play well and score goals.
"Against Bolton we defended fantastically, so our defenders will have gone into the dressing room and then to the hotel thinking about their performances and what they did well.
"The goalkeeper (David Marshall) did fantastically again, and Fraizer and the forward lads will be thinking about the goal that was scored and the good moves we put together. You can only get confidence from performances and results."
Solskjaer admits it has been a "dream" of his to return to United, who he played for between 1996 and 2007, as a Premier League manager and that he had swiftly scoured the fixtures to see when it would happen once he landed the post at Cardiff.
"I looked at it the day I got the job - when we were playing Man United," the 40-year-old former striker said.
"Since then it has been so busy, I haven't had time to think about it. But now, my focus is of course on that game. It is a dream."
When that dream is fulfilled on Tuesday, Solskjaer may well find his team having to handle United's new record signing Juan Mata, with the playmaker having completed his switch from Chelsea on Saturday for £37.1million.
Regarding the Spain international, Solskjaer joked: "I think he will have to wait until next weekend to play for United - well, hopefully he will!
"He is one of the top players in European and world football. He has done fantastically for Chelsea over the last few years. United have signed a top, top player."
Solskjaer, whose side are currently bottom of the Premier League, made five changes to his starting XI for the cup tie, opting to drop the likes of Steven Caulker and Gary Medel to the bench for a rest along with Noone and Campbell.
He said he had anticipated that Bolton - currently 18th in the Championship - would prove tricky opponents, though, particularly given they were looking to bounce back from a 7-1 defeat to Reading last time out.
And certainly Wanderers boss Dougie Freedman thought his men had done a good job of making life difficult for the visitors.
"It was a spirited performance and there wasn't a lot in the game," Freedman said.
"It was decided by a goalkeeping error, which is difficult to swallow - the defeat wasn't anything to do with our performance in general.
"I felt we defended well and created opportunities. A Premier League side had to change the way they were playing in the second half to try to cope with us going forward.
"We have been working on our defensive duties all week, and this was a fantastic response to what happened at Reading."