Moore could have had a hat-trick in the first quarter, firstly shooting just over after robbing Killie centre-back Mark O'Hara and then slicing a volley wide from 12 yards following a cross.
The 19-year-old's best chance came when Paul Lawson's ball played him clean through but he shot just wide.
Moore has already signalled his goalscoring prowess with seven goals in 11 starts for Cowdenbeath on loan last season and with a wonderful 25-yard strike against Hearts last month with his first touch of Scottish Premiership football.
And he showed other sides to his game against Killie, notably when his backheel set up substitute Lionel Ainsworth for another chance that went begging.
John Sutton finally converted for Motherwell when he sent a diving header past Craig Samson following a 54th-minute breakaway and Henri Anier came off the bench to create a goal for himself with two minutes left.
And McCall was delighted with Moore's contribution to a victory that sent Motherwell back up to third spot.
McCall said: "I thought that was probably as good a debut (as I have seen) without scoring a goal. He was terrific. He's a strong, little hard boy. "He is just infectious and obviously Henri has been away for a couple of international games with Estonia.
"We had to say to him at half-time don't let that (missing chances) affect you, keep getting into the positions. He was a great foil with Sutty. It would have been nice for him to score but he was a real key part of our performance.
"He was first team on the team sheet because not only has he done it when he has come on as sub, he has done it for the under-20s and in training he has been terrific. "He merited his chance and hopefully he will kick on from there."
Sutton believes Moore will not have to wait long for his second Motherwell goal.
Sutton said: "I thought his general play was very, very good. From a striker's point of view you would rather be getting in there and missing the chances, and he certainly got in there. "With the quality of finishing he has got, he will score a lot of goals. You can tell the way he shapes up to hit the ball, he is a good finisher.
"For a small guy, he held the ball in really well. He is not easily pushed off the ball and he did really well for the team getting us free-kicks and pushing us up the pitch."
Kilmarnock manager Allan Johnston bemoaned his side's slack defending, especially the absence of marking that allowed Sutton to head home.
But he was also encouraged by youth as 19-year-old midfielders Craig Slater and Chris Johnston vindicated their elevation to the team.
"One of the plusses was young Craig Slater, I thought he was brilliant in the middle of the park," Johnston said.
"He has been like that in the under-20s and he deserved his chance. Young Chrissy Johnston as well was really direct and looked really promising."
Johnston refused to put any blame on Kris Boyd for missing a free header that would have brought Killie level and he brushed off questions on the thorny issue of Reuben Gabriel.
A Twitter account purporting to be from Gabriel last week criticised Johnston and the club for the continuing failure to play the Nigeria international and the club were forced to deny claims they had not paid the player.
When asked whether he knew who had written the comments, the Killie boss said: "I don't really know. I think we have enough on our plate with football rather than worrying about a few tweets.
"We need to sort out the defence rather than worry about other things."