The online firm enhanced the odds of United, Bournemouth and Derby all winning to 6/1 and it was only the Cherries who gave cause for alarm, as they fought back to beat Stoke 2-1.
Leaders Manchester City had earlier been held to a 1-1 draw at Burnley but, despite United's victory, are still 13 points clear.
Romelu Lukaku made the breakthrough on 55 minutes with a close-range finish before Sanchez - who joined the Red Devils from Arsenal ahead of the transfer deadline in a swap deal for Henrikh Mkhitaryan - doubled the lead on 68 minutes.
The Chile forward saw his penalty saved by Jonas Lossl but was alert to knock in the rebound.
On another day, Arsenal may have been made to miss their former star man but that certainly wasn't the case as they thrashed Everton 5-1.
The Gunners were as outstanding as Everton were poor in the first half, although Pierre-Emerick Aubameyang was offside when he scored Arsenal's fourth just before the break.
Leicester and Swansea drew 1-1 at the King Power Stadium.
The Foxes were again without forward Riyad Mahrez, who had missed training in the wake of a deadline-day move to Manchester City falling through.
Jamie Vardy gave Leicester the lead on 17 minutes and Swansea lost midifleder Leroy Fer to what looked a serious ankle injury after 34 minutes.
But the visitors, who had beaten both Liverpool and Arsenal to boost their survival hopes, equalised on 53 minutes through Federico Fernandez's header.