The Steelmen went behind early on thanks to an Oli Shaw strike, but rallied in the second half and turned the game on its head.
Devante Cole and Bevis Mugabi scored the goals that meant Motherwell claimed their first points from a losing position this season.
"The game is in your head," Alexander insisted. "When you're on a difficult run for a long time, it's hard to get yourself out of that hole.
"We challenged the boys at half-time to turn everything on it's head, and we had to do that.
"Coming here, not playing as well as we could have and getting beat would have been a big blow to us.
"I'm so pleased for the players, because I've seen the work they've done over the last three weeks - they deserved a reward at the end of it.
"We got that tonight, and it has to be a catalyst now - it has to mean more than just three points, it has to be the start of something better."
Motherwell's goals came from a goalkeeping error, and then a simple corner routine.
Ross County manager John Hughes was left disappointed with how easily Motherwell appeared to break through their defence.
"I'm disappointed with the goals we lose, because I don't think teams have to work too hard to score against us," he said.
"We have to make that better, and we have to stick together.
"I'm really disappointed with the result. I felt that if we could have hung on there in the second half then we might have just got away with it, but it wasn't to be.
"We can't keep losing the goals we've been losing, it's as simple as that."