The lead was doubled in the 20th minute, and this time it was Sanchez who got on the scoresheet.
Swansea were beaten 4-0 away in United's first away game of the season, with Lukaku and Pogba scoring as well as getting an assist.
Not until the hour mark was David de Gea called into action, the Spaniard making two excellent stops from Tammy Abraham in quick succession as the visitors enjoyed their first spell of pressure.
United didn't have a flawless afternoon, however, as the side appeared to lose focus in the second half and gave away several good chances.
"In the first half they didn't cross the line, didn't have one shot, we pressed so high and so strong, recovered the ball, had lots of movement and passing, we arrived in many risky positions, we should score one more".
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Liverpool were unable to hold onto second place as United moved two points ahead of them at Old Trafford.
Leicester midfielder Wilfred Ndidi was sent off for a second caution with three minutes left but Jamie Vardy slotted in during added time.
Despite the many accolades he's earned in recent years, De Gea is still yet to win the Premier League Golden Glove award for highest number of clean sheets.
Barnes fired seventh-placed Burnley ahead in spectacular style in the 22nd minute with an acrobatic volley from an Aaron Lennon cross.
Striker Dwight Gayle had several good chances in a first half dominated by Newcastle but he failed to find the back of the net. The second half was different.
'We deserved to feel second in spite of what you can say, the critics you make, you all say the third, fourth, fifth, sixth are better than us but they are not better than us because we have more points than them.
Huddersfield Town remained in trouble, three points above relegation, after losing 1-0 at Newcastle United to a goal by Ayoze Perez.