Marcus Rashford’s strike moved United to just one point behind their fourth-placed rivals as the race for the Champions League spots enters the home straight.
And Old Trafford chief Van Gaal says his side are poised to strike after winning the derby he claimed was do or die for their top-four hopes.
He said: “I have said that we must win this game and we have done it so I am very happy because otherwise the gap was too big if they won.
“A draw and the gap was still four points then it is very difficult. Now it is in our hands.
“We have to win our games. We have more home matches than away matches and we don’t lose often at Old Trafford.
“I have seen the dressing room after the match and it was fantastic with the happiness in there.
“I don’t think we have had a lot of luck this season and now we have a big result against Man City at the Etihad Stadium to go one point behind, equal with West Ham.
“And when you have more home matches than away matches you have a big possibility. The players feel that.”