Bruno Fernandes prodded the Reds ahead, after Robert Sanchez was sent off for the visitors, and Casemiro's header put Ruben Amorim's men firmly in the driving seat.
Casemiro's second yellow card evened things up at 10 v 10 and the Blues gradually grew into the game before reducing the arrears with a header by Trevoh Chalobah.
Thankfully, United held out to take maximum points, and it was a welcome conclusion for experienced left-sided central defender Shaw.
"It was massive, I think we spoke a lot about the game and before the game about winning, that was the most important thing today," Shaw told Sky Sports following our victory.