Despite a tumultuous recent period at Tynecastle, Hearts moved into the top half of the table, above United, as Ryan Stevenson scored twice in the first half, the second a penalty.
"The SPL is a crazy league this year," said McGlynn. "We've not been that consistent, but when you get three points it makes such a big difference. We're delighted to get into the top six.
"We're delighted that over the start of these four games coming up we've won the first. We go down to Rugby Park on Wednesday, which will be difficult.
"It's nice to get three points on the board tonight and go down there with a feel-good factor and some confidence."
Hearts' Edinburgh rivals Hibernian have been praised for turning from relegation candidates last term to top-six hopefuls this season, yet McGlynn's men are only three points behind.
McGlynn hopes Hearts can overtake Hibs come the Edinburgh derby early in the new year.
"We'd like to be in that position come January 3," he said.
Try as they might United could not breach Hearts' defence for a second time after Keith Watson's 57th-minute strike.
"Over the piece we just deserved it," McGlynn said. "Today we were delighted to get the early start. John Sutton was causing problems up front and that's where the first goal came from.
"It gave us a great start and the penalty Ryan slotted away very well. United were never really out of the game. We have got a good defensive record and that had to come out in the second half when we came under pressure."
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