John Sutton's first-half double put the visitors in control, but Melvin De Leeuw responded as County piled on the pressure after the break.
Motherwell, who had debutant Dan Twardzik in goal, held out to recover from last week's hammering by Celtic and stay fifth in the Premiership.
And McCall said: "They threw everything at us second half. It was probably a tale of two halves and the first-half performance got us the victory.
"I wouldn't say we were lucky, more hard-fought and we stuck in there when we needed to.
"I thought our young keeper did well in difficult circumstances. When you get into a 2-0 lead you need to try and kill the game off but they had a real go.
"There's all different ways to win and that was gutsy and I'm delighted to get back on the winning track."
County have won just one point since October 5, and boss Derek Adams cut a frustrated figure afterwards.
He said: "We totally dominated and obviously deserved to win. We battered Motherwell and came away with nothing - we should have won by four or five goals with the chances we had.
"If he's honest enough then Stuart McCall will say his team got off today because we should have put them to bed in the second half.
"We should never have been two down, they got a deflected goal and we believe the second might have been offside.
"There wasn't too much in the first half apart from that and we had a goal disallowed in the second half for a foul in the box.
"They cleared a few off the line and their keeper made a few good saves. We put balls across, over the bar and past the post at open goals. We should have scored and a few goals wouldn't have flattered us."