Chris Erskine opened the scoring for Partick before the Motherwell hit back through Keith Lasley and Lionel Ainsworth added a second for the Steelmen after the break.
Kallum Higginbotham, who was on loan at Motherwell last season, turned the match in Partick's favour with two goals, but late strikes from John Sutton and Stephen McManus completed the home side's fightback.
McCall admitted his players were forced to dig deep for the win and gave Partick credit for playing their part in an exciting encounter.
"When we went 2-1 up I thought we were back in it but the penalty gives them a boost before Higginbotham's terrific third goal," said McCall. "They showed great character and so did we and the action was end to end.
"I stressed to the players that we might make the most of set-pieces and Sutton and McManus were terrific in the air for the last two goals.
"In the end I was delighted with the victory, and the fact we got the game on, but we had a lot of heavy legs on a heavy pitch.
"We were a bit rusty at times and although it was not our best performance we kept going."
Alan Archibald was frustrated with his Thistle side after they let victory slip away in the closing stages.
"I thought we were worth at least a point, particularly the way we played in the second half," he said.
"We dealt well all day with the Motherwell threat until the last five minutes but our Achilles heel came back to haunt us again.
"Kallum Higginbotham was outstanding in the second half and for us to score three goals at Fir Park, it should be enough to win the game as not many teams do that.
"They are not young boys any more and when you are 3-2 up you have to manage the game.
"We had to make substitutions but Motherwell are very good at it and threw everything at us - but we should be able to see it out."