Motherwell looked bright in the opening stages and Alan Combe had to produce a brilliant save in the 15th minute to deny Brian McLean.
The tall defender met Richie Foran's knock back five yards out and the keeper had to change direction to dive and claw the ball over the bar, a world-class save.
Unfortunately, Combe took a knock making the save and had to be replaced by Graeme Smith.
Killie had their first attempt in the 23rd minute when Well's Steven Hammell had to be alert to clear Fraser Wright's header off the line.
Well continued to enjoy the better of the half, but it was the home side that took an unexpected lead in the 34th minute.
Wales leapt like a salmon to beat Stephen Craigan and looped around strike partner Colin Nish to collect his perfectly weighted lay-off before firing home low to the keeper's right-hand corner from the edge of the box.
Hammell came within inches of levelling the match in the 39th minute when his 20-yard free-kick clipped the post.
Killie increased their lead six minutes into the second half with Wales' second goal.
Again Nish provided the assist, his challenge on Well keeper Smith from Aussie debut boy Lindsay Wilson's high cross adjudged legal by Stuart Dougal, and Wales pounced to slam home his fifth of the season.
Motherwell's luck was out again in the 72nd minute when they were denied again by the woodwork.
Scott McDonald turned sharply inside the box and his shot beat Smith, but rebounded of the post. McLean should have done better a minute later, but his unopposed header bounced meekly wide.
McLean was denied for a third time in the 81st minute when it was Smith's turn to produce a great save to block his powerful header.
Motherwell's hopes of a comeback were dashed two minutes later when debutant substitute Abel Thermeus lashed out at Wright and was shown a red card.