Killie defeated Celtic in last season's Scottish Communities League cup final, but their celebrations were cut short by the sudden death of midfielder Kelly's father, Jack.
Former Celt Cillian Sheridan gave Kilmarnock the lead before a second-half penalty from Kelly wrapped up their first victory in the east end of Glasgow for 57 years.
Shiels said: "I am happy for the supporters. The boys created history today.
"Two generations of supporters haven't experienced a victory here for Kilmarnock and it makes me so proud to hopefully give them some satisfaction and help them to enjoy their weekend.
"But the person I am happy most for is Liam Kelly. He didn't get a chance to truly celebrate beating the best team in Scotland in the cup final in March.
"It was silent in our dressing room in March but today there was a freedom of celebration, we have beaten the best team in Scotland and there is no better feeling.
"We have the chance to celebrate now without feeling guilty about it. That is a monkey off my back and I am sure it is for the players.
"I said that to them in the dressing room - 'Please enjoy yourselves tonight'."