The Red Devils recorded a key win to move back above Arsenal into the Champions League spots, while they now trail third-place Tottenham by only three points after Spurs failed to win any of their last three games.
United did not have it easy however, in a see-saw encounter that saw them initially fall behind to a spectacular Yan Valery strike before equalising through Andreas Pereira’s top-right corner effort.
Romelu Lukaku game them the lead soon after, before James Ward-Prowse’s free-kick 15 minutes from time brought them back to level footing again.
But Lukaku's second late on put an end to Saints' resistance, and Dalot – who gave a good performance as a second-half replacement for the injured Alexis Sanchez – felt it was a quintessential United display.
“This is Man United,” he told the club’s official website . “When you're 1-0 down, we know the crowd always pushes for us and we wanted to win it.
“I think the badge speaks for itself when we talk about comebacks, desire and attitude, and for us it was just another game that we gave everything in.
“It was like a two-second punch in the stomach when we conceded that second goal, it was a good goal too, which David [de Gea] had no chance with.
“But we knew we had maybe 10 minutes more and, like I said, it's Man United and we wanted to win it, and Rom got us the other goal.
“It's always a pleasure to play in this stadium and what a game to win with such a great comeback. It was unbelievable.”
Up next for United on Wednesday is the Champions League last-16 second leg away to Paris Saint-Germain, who won 2-0 at Old Trafford last month.
Dalot insists United go into it with no fear, however, as they have nothing to lose.
“We have no pressure on us [on Wednesday] because we are 2-0 down, but we know in football anything is possible and, in this club, you know that even more," the full-back said.
“We feel that if we can score a goal, then they will be worried, so we will focus on doing that.”