Scott McDonald, Lee Erwin and Lionel Ainsworth found the target to consign St Mirren to relegation and Killie to a seventh consecutive loss, which leaves them three points and seven goals better off than Motherwell with two games left.
Motherwell are at St Mirren Park next week while Killie have Partick away and Baraclough feels his side are breathing down the necks of Gary Locke’s men, while Ross County could still be involved if they fail to beat St Mirren on Saturday.
When asked if the result puts the pressure on Kilmarnock, Baraclough said: “I think Gary would have been feeling that anyway and that drags us closer.
“What happens in those situations, all of a sudden players get edgy, make decisions that you probably wouldn’t do normally, fans get edgy.
“I feel as though we are a side that are in the ascendancy.
“It’s all to play for. There are two massive games now for both us and Kilmarnock and it gets us closer and they know we are on their tails.”
Locke admitted his side were in the middle of a relegation battle.
“We knew if we got a result tonight we were okay. The fact that Motherwell have beaten us, we are right in the mix,” he said.
“No point feeling sorry for ourselves, we have got to make sure we respond.
“We have been on a terrible run and we have to rectify that next week.”