Skelton opened the scoring for Kilmarnock at Tannadice
Kilmarnock went top of the Scottish Premier League with a clinical victory over a disappointing Dundee United.
Last season's second-bottom side survived an early Garry Kenneth volley that struck the Killie crossbar.
But former Gretna midfielder Gavin Skelton headed the visitors into the lead just before the break.
United had dominated until then, but Killie went further ahead after the break when Danny Invincibile finished from 12 yards to end worthy winners.
The victory lifted Killie three points clear of Celtic and Rangers in the league table - at least until the Old Firm sides meet at lunchtime on Sunday.
Renewed question marks about the future of Darren Dods will emerge after the United defender was not even included on the bench following a failed transfer approach by his former club, Inverness Caledonian Thistle, this week.
A midweek hat-trick could not prevent striker Jon Daly being dropped to the bench along with David Goodwillie, who scored a double in the Co-operative Insurance Cup tie with Cowdenbeath, and Craig Conway.
Simon Ford missed out through injury for Kilmarnock and the reshaped visiting defence were under pressure immediately as United threatened to match their high-scoring cup exploits.
But Kenneth's 35-yard piledriver rebounded off the crossbar with only two minutes gone as Kilmarnock maintained a record of not losing a goal this season - their best defensive run in eight years.
Warren Feeney, who had come into the United side along with Lee Wilkie, Francisco Sandaza and Danny Swanson, beat the Kilmarnock offside trap but screwed his shot across the face of goal and well wide.
The game became bogged down in midfield, but it was United who were dominating possession until they were hit by a sucker-punch four minutes before the break.
Invincibile (centre) secured an important win for Kilmarnock
Fit-again David Fernandez, restored to the side along with David Lilley, whipped in a cross following a short corner and Skelton, making his first start of the season, headed home.
Sandaza fired wide as United tried to respond immediately, but Craig Levein's side were proving as toothless as they were deadly in midweek.
Conway replaced the out-of-sorts Willo Flood eight minutes after the break.
But it was Killie who went further ahead after 59 minutes, when Mehdi Taouil's fine through ball set up Invincibile to fire home from 12 yards.
Levein threw on midweek heroes Daly and Goodwillie in a desperate attempt to salvage at least a point.
But the side tipped by many to be the third force this season behind the Old Firm continued their miserable start to the league campaign.
Dundee United manager Craig Levein:
"It was just one of those days. The first half, we played the ball fantastically well and the big disappointment was the final delivery.
"I think Kilmarnock had two shots at goal in 90 minutes.
"Francisco Sandaza made his first start and maybe, as he is not 100%, coming on as a sub is better for him.
"I am really pleased with the way we played, but we got hit with two sucker punches."
Kilmarnock manager Jim Jefferies:
"We knew it would be a tough game as they gave Celtic a hard time up here, but I thought our defence was magnificent.
"I thought our tactics worked. We brought in Gavin Skelton to have four across the middle instead of playing big Conor Sammon up front as the two boys who could take the ball into feet was going to be uncomfortable for them as United like the aerial battle.
"So that's the reason we played Mehdi Taouil and David Fernandez up front and they held the ball up well for us.
"This will give them a massive confidence boost as everybody was tipping Dundee United to be up their challenging for third."
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