United travel to Crystal Palace on Wednesday night 15points adrift of runaway leaders Manchester City and will hope to close that gap further in Sunday's derby at the Etihad.
Solskjaer has consistently played down talk of a title challenge but wants his players to be ready to take advantage of any slip by City, as Stewart did for the first of his 27 career Grand Prix wins.
Stewart won the 1965 Italian Grand Prix after leader Jim Clark suffered a mechanical breakdown on the final few laps and team-mate Graham Hill made a wrong move while close to the finish.
"That’s just what we have to do. We have to go all the way. Don’t think about City, don’t think about the points tally. You’ve got to go every single game step by step," Solskjaer said.
"Jackie Stewart’s first win in Formula One. I think we’ve all heard about that one. You never know what’s going to happen in life and definitely not in football and sports.
"Do our job and don’t have any regrets when the season is over - just pick up as many points as we can, play as much as we can and improve as much as we can."
United will hope to have Paul Pogba back to full fitness if they are to close in on City during the final months of the season, and Solskjaer believes the midfielder could return from a thigh injury before the March international break.
Pogba has not been available for selection since coming off injured in the 3-3 draw with Everton at the start of last month.
Solskjaer said that Pogba would not return until March at the earliest, but the 27-year-old was ruled out of Wednesday's trip to Crystal Palace.
When asked whether United fans will see Pogba return before the internationals, Solskjaer said: "I hope we will, definitely, and he’s very positive. He’s working really hard.
"He knows when he gets back we haven’t got two or three games to play him into form so he’s working hard on his fitness and when you’ve got the quality of Paul, fitness is the main thing.
"Mentality wise ... you know when the sun is out in Manchester there’s nothing to complain about."