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Murphy opened the scoring after 11 minutes when he drove at the home defence and slotted the ball beyond Cammy Bell.
Gary Harkins restored parity for the home side on the half-hour mark, however the deadlock was only to last five minutes, Murphy racing on to Michael Higdon's excellent through ball before rounding Bell and slotting into the net.
McCall was pleased to see Murphy notch his first two goals of the season and believes that he has coped well with the pressure placed on him over the last few years.
"I'm really pleased for that kid, he's a cracking lad and is totally committed to do his best for Motherwell," he said.
"I was hoping Jamie would come back from his summer break fresh and energised and that has been exactly the case.
"We tried him out in a different position today behind Henrik (Ojamaa) and Higgy (Higdon), it worked well and he got two terrific goals.
"He's had a lot of pressure over the last two seasons in regards to will he move? Will he be picked for Scotland? And for a young guy that can be a lot of pressure, so he has just got to focus on his football."
Motherwell sit joint top of the Clydesdale Bank Premier League table after registering their first win of the season.
McCall was pleased at the threat his side presented on the counter-attack as well as the way in which the younger players within his squad have blended into the first-team.
"I'm delighted, not only with the victory but the way we went about it, I was informed after the game that we finished the game with eight players under the age of 22," said McCall.
"We always get good games against Kilmarnock and that was my first win against them in my time here as manager - it's good to get that monkey off my back.
"I felt we were always a threat on the break and I think we deserved the victory in the game."
Despite his satisfaction at picking up all three points, McCall was disappointed to lose the services of Simon Ramsden who hobbled off in the first-half with a hamstring injury.
The former Bradford defender will now miss Motherwell's Europa League fourth round qualifying clash with La Liga side Levante.
"Simon has strained his hamstring, we are not sure how long that will rule him out for but he certainly won't make the Levante game," added the former Bradford boss.
"We also had to take off Chris Humphrey and Nicky Law as they had slight injuries, but they will be ok for Thursday evening."
Kenny Shiels felt Kilmarnock lacked a cutting edge as they fell to defeat.
The Northern Irishman believes the absence of Paul Heffernan has come as a big loss for Killie's attacking threat.
"I think it could have went either way, we were playing against a counter-attack team and we knew going into the game that Motherwell are a dangerous team away from home," said Shiels.
"It was poor play for the first goal and the second the player wasn't tracked, we have to look at the imagination side and work on that in the next week.
"We need someone to hold up the ball a bit better and link it up, we are missing Heffernan and you can see how it has an impact on our performance.
"It's early yet and too early to make assessments, it could have so easily been a draw today but I still feel if you take Harkins out then we lack creativity."
