John Sutton's early strike earned Motherwell their first home win of the season and halted Partick's unbeaten start to the campaign.
A fine second-half performance from Alan Archibald's visiting side put Motherwell under pressure and meant Partick could consider themselves unlucky to leave Fir Park with no reward.
It was the narrowest of victories for the home side and on the bulk of the play was probably deserved, despite Thistle dominating the closing stages.
McCall said: "I was delighted with the win especially the first half as we stopped them playing. We knew a second goal would kill them off and their 'keeper has had a couple of terrific saves.
"However when you don't get a second the game is still there to be won and give credit to Thistle who made a right good go of it in the final 20 minutes."
The 'Well boss admitted to having a few anxious moments and added: "They put us under some pressure and gave us a few scares but overall Lee Hollis has had very few saves to make and we could have finished it off, especially the chance that fell to Keith Lasley who should have scored from 8 yards.
"But it was another clean sheet for us and the two wins, of 1-0, out of four games and if that is the way it has to be then fine."
Although Thistle finished on top, their unbeaten run come to an end, and boss Alan Archibald was honest enough to admit his team did not quite do enough.
He said: "It is not nice to taste defeat for the first time and it is a sore one to take but we didn't turn up in the first half.
"Although we were better in the second, 'Well had a game plan and pressed us in the first half.
"We played the game at our tempo in the second and attacked their goal and probably did enough for a point but we might have been picked off for a second."