Motherwell were level three minutes later when the unmarked Henri Anier slotted home after Keith Lasley's through-ball and they capitalised on some late first-half pressure when John Sutton netted from close range after Kilmarnock centre-back Jackson Irvine had taken a fresh-air swipe at Simon Ramsden's cross.
Craig Samson saved brilliantly from Sutton's header just after the restart to leave the game finely in the balance and Kris Boyd came close to an equaliser from several half-chances before Ramsden's 87th-minute red card gave the visitors fresh hope.
Johnston, whose team have two points from five games and lost to Hamilton in the League Cup, said: "The good thing is that you can see we're not far away. If we start cutting out the mistakes then we will definitely win a lot of games but we need to defend better individually.
"The timing of the goals was a killer and that sums up our luck in the last few games. But the boys will take a lot of confidence from the performance and hopefully we can start turning that into wins.
"It's just not going in for us, it's bouncing about the goalmouth, the keeper is saving it. I'd be more worried if we weren't creating chances but we are playing good football and we're just that wee fraction away. But you can see we are improving every week."
Johnston introduced Michael Gardyne in the last quarter and believes the loan signing from Dundee United will provide extra creativity.
Johnston, who is still looking to bring in two players, including a centre-back, said: "You can see his quality when he came on there linking the play. I think he and Boyd will be a really good partnership."
Motherwell manager Stuart McCall praised Hollis for repelling the pressure after the "poor decision-making" from Ramsden, who was booked for complaining about a rejected penalty claim when barged by William Gros before getting a second yellow card for a late tackle on Rabiu Ibrahim.
And he was delighted to see his team move into third place on nine points despite not yet firing on all cylinders following a summer of transition.
McCall told MFCTV: "There are a lot of different ways to win a football match and the most important thing is getting the three points.
"A few of us can play better but I still thought there were a lot of good individual performances.
"Lasley in the first half was excellent and (Stuart) Carswell took up the mantle in the second half.
"Big John Sutton was a tirless worker and I'm glad he got the winner, and obviously Lee Hollis at the end.
"Although we have not fully clicked yet, we will take six points out of six any day."
- Sports & Recreation
- John Sutton
- Simon Ramsden
- Lee Hollis
- Keith Lasley
- Kris Boyd