However, the home side's hopes of a revival were all but ended two minutes before the break when Larsson was sent off for a risky lunging challenge on Ander Herrera.
United almost went ahead after 29 minutes, but Jordan Pickford produced a fine save to keep out Jesse Lingard's effort from 20-yards out.
Sunderland have lost five of their last six games and failed to score for the seventh consecutive game, a desperate run of over 11 hours.
Victory saw United close to within four points of Manchester City, who occupy the fourth and final Champions League qualifying berth and have played a game more than Mourinho's side. And that's only because they beat Sunderland on Sunday.
He said: "We keep fighting, we keep going". The midfielder slid into a challenge against Ander Herrera and received a straight red.
The Red Devils boss also stated that it could end up being a blessing in disguise as far as their Europa League efforts are concerned.
Dead balls looked Sunderland's best hope so Bryan Oviedo's tame free-kick from a decent position was wasteful, with the first real test for Sergio Romero - filling in for the injured David De Gea - when Lee Cattermole took aim from distance.
One person dead after shooting near mall in South Florida
Their identities are believed to the the gym's general manager Jeanine Ackerman and a personal trainer named Mario. One person said she was waiting to see if she would be allowed back inside to retrieve her belongings.
United went into the game at the Stadium of Light without a number of first-team players but managed to record a comfortable 3-0 victory against the Premier League basement boys.
It was vital for United to win at the Stadium of Light after back-to-back home draws to keep in the hunt for a Champions League spot through the Premier League.
Shaw recovered from an early booking, awarded for flying in behind on Didier Ndong, to offer more width and attacking threat down the left.
Ibrahimovic's opening goal was a delight, spinning away from Billy Jones before bending home from outside the area.
The full-back was a surprise inclusion in the starting line-up and set up Henrikh Mkhitaryan's goal in what proved to be a routine win over the league's bottom club, who had Sebastian Larsson sent off in the first half.
If Mourinho was to write down the qualities required of his ideal left-back, he would have pace, confidence to go forward, be good in attacking areas, strong in the tackle and defensively astute: basically, a modern-day version of Ashley Cole.