The midfielder was the hero on Saturday afternoon with a terrific free kick in injury time that ensured a dramatic 3-2 victory at Rugby Park.
The win allowed Gary Locke to celebrate a positive start to his tenure after taking over as interim manager until the end of the season, following the recent departure of Allan Johnston.
Clingan said: “The dressing room was really upbeat afterwards. Everyone was high-fiving each other and now we’re just looking forward to the next game.
“It’s probably the most important goal I’ve scored since I came here – and the most satisfying. Coming from behind twice was excellent and to cap it all off with that goal was great. You’d have thought that we’d won the cup the way that win was celebrated but we just want to do well for ourselves and the new manager.”
United appeared to be on course to extend their unbeaten run to eight games when they took the lead after just three minutes thanks to an early penalty by Nadir Ciftci.
But Kilmarnock refused to be disheartened and Josh Magennis quickly equalised for the home side.
The visitors were back in front when Henri Anier netted his first goal for the club. But Kilmarnock levelled for a second time through Chris Johnston’s second-half strike.
Clingan then had the final say with a superb free kick deep into injury time to claim all three points. And he said he had a feeling he was going to bag the winner as soon as he stepped up for the set-piece. He said: “To be fair, when we were given the free kick, I really fancied it. Sometimes you get one and you think ‘I really want this one’. I didn’t know it was in the last minute of the game, which just made it even better.
“We were just really pleased with our performance. We gave away some silly goals but, overall, I thought we were fantastic. Our second-half performance was one of our best this season.”
United manager Jackie McNamara was unhappy with the inconsistency shown by his own side.
He said: “It’s a tough one and disappointing. The three goals we lost were very poor to say the least. In the first half, I thought we were excellent and could have had a few more goals.
“We were all linking together, there was good movement and we looked like we could score every time we went forward. But I thought we were far too deep at times in the second half.”
Paul Dixon made his second debut for United, while new Killie signing Nathan Eccleston was named among the substitutes at Rugby Park.
Kilmarnock endured the worst possible start to the game when they fell behind after just three minutes.
Alexei Eremenko was judged to have fouled John Rankin in the box and Ciftci stepped up to dispatch the spot-kick into the bottom corner.
The home side refused to be discouraged and were back on level terms seven minutes later. Eremenko’s free kick was knocked into the path of Magennis and his effort was allowed to trundle over the line, beating goalkeeper Radoslaw Cierzniak.
But, in an action-packed opening spell, United edged in front again with 14 minutes on the clock. Chris Erskine released Anier through on goal and he kept his cool to lash home his first goal for the club from just inside the box.
United could have been further ahead when a cross from the left by Dixon almost found its way into the back of the net and was cleared off the line by Chris Chantler.
Anier and Ryan Dow both attempted to follow up but their efforts were blocked before the danger was eventually cleared by the home defence.
At the other end, a back-post header by Magennis was begging to be tapped home in front of goal but there were no takers from the home side.
Killie were out of the traps quickly after the break and Cierzniak was called into action to block a Magennis header.
They were back on level terms again after 52 minutes when Tope Obadeyi picked out Johnston in front of goal. Johnston unleashed a drive that initially appeared to be blocked by Cierzniak, only for the ball to slip under the goalkeeper and over the line.
Just when it looked like the points would be shared, Clingan grabbed the winner in injury time with a superb free kick from just outside the box.