Marcus Pedersen gave Norway the lead before half-time, pouncing after defensive errors from Senegal in a first half Norway dominated territorially.
The real damage was done early in the second half. Haaland received Martin Ødegaard's throughball and finished compositely while falling to the ground to make it 2-0, then Sarr pulled one back with a tidy finish to give Senegal a foothold.
Haaland settled Norwegian nerves five minutes later with a sharp opportunistic strike, before Senegal pressed in the closing stages and twice came close to finding what would have been an equaliser.
They were denied until stoppage time, when Nicolas Jackson set up his Crystal Palace teammate for a second Sarr goal that finished 3-2 but could not force the fightback the Lions of Teranga needed.
Haaland now has four goals in two World Cup appearances. He spoke candidly about his enjoyment of the tournament.
"It was special again. Another amazing night and I'm super proud. I'm enjoying it a lot. I've enjoyed playing for Norway ever since my debut and you can see that. The World Cup is nice!"
For Senegal, the result leaves qualification requiring a win against Iraq in Toronto on June 26. Sarr did not hide his disappointment while maintaining belief.
"It was tough. We're a little disappointed. But it's not over yet, there's still a third game to play. We're going to go there to win it, and we're going to work hard."
Norway face France in Boston in four days, a match that will determine who tops Group I.