City have soared 10 points clear of their local rivals thanks to an 18-game winning streak in all competitions.
United’s own inconsistent form has helped open up the gap, but the Red Devils beat Newcastle 3-1 on Sunday to win for just the second time in six league games.
“We’ve got to be there just in case,” said Solskjaer. “Every time we get three points we’ve done our job and that’s what we’ve got to do and see what other teams do.”
Solskjaer made five changes to the side that impressively thrashed Real Sociedad 4-0 in the Europa League on Thursday and was lucky not to be punished for a disjointed start from the hosts.
“We had to find a way to win it in the second-half. The first-half wasn’t up to the standard that we wanted,” added Solskjaer.
“Maybe because of Newcastle, maybe because of what we did in the week. We asked them to go again after a high-intensity game and it took us to half time to get our legs and energy.”
A run of two wins in 14 games has left Newcastle just three points clear of the drop some, but Steve Bruce remains confident his side will survive.
“Fulham have had a good week and won a couple of games, which at the bottom end of the table is big, but there are a few of us: Brighton, Burnley and maybe Crystal Palace looking over their shoulders,” said Bruce.
“My message to the supporters is that I’m convinced we’ll be ok.”
After a blistering start to his United career last season, Dan James has struggled for game time, but the Welshman has now scored in his last three appearances as he blasted past Darlow from close range just before the hour mark.
Darlow had saved the only spot-kick Fernandes has missed as a United player when the sides met earlier in the season.
But he was wrong-footed this time as the Portuguese playmaker coolly converted to give United the two-goal cushion they craved.