Two goals just before half-time gave Sutton a advantage, this was followed up by Lewis Montrose being sent off for the visitors but a late goal made it a nervy last few minutes, writes Tom Feaheny.
The results moves United up to fourth in the table and just two points off top.
"At 2-0 up I felt it could have been a more comfortable afternoon, we had chances but we weren't at our best, it was a case of good individual play," said Doswell to the club's website.
"We had control, we hit the post and the bar, had a chance, were missing by fine margins, we were on top, they got the goal back, thankfully we could see it out, the most important thing is three points."
One player who Doswell picked out for praise was keeper Jamie Butler, who made a late save to ensure their victory.
"Jamie has been fantastic, his disruption is exceptional, he has fitted into the group, we lost Ross Worner with his knee injury, that was a big blow so Jamie has done a fantastic job."
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