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, whose side next play at Kilmarnock on Boxing Day. "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."
He added: "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.
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."
Dundee United manager Peter Houston was frustrated his side returned north empty handed.
"I thought the team that played the better football lost today," he said. "We played quite well in the first half as well and again it comes down to an individual error. The first goal Brian (McLean) should deal with, we didn't deal with it properly and we found ourselves a goal down.
"We were the away team today, but we pinned Hearts back and they were desperately hanging on. They cleared everything we threw into the box, but I'm walking away from here with nothing and I feel a wee bit hard done by. The ball didn't break for us today."
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- Ryan Stevenson