Callum Slattery’s brilliant 25-yard shot put the Steelmen ahead early on and, after Regan Charles-Cook’s 39th minute strike for County, Tony Watt slotted home a late winner from a Ricki Lamie pass.
Alexander, whose fourth-placed side are now unbeaten in their last six Scottish Premiership matches, said: "Callum’s goal was a brilliant strike and Tony finished well from what looked to me a tight angle.
"He hit the target and won the game so it’s great to reward the support we had in the stadium today which was brilliant, really bouncing.
"And the players deserve it because we know we didn’t play as well as we know we can. But we still produced a winning performance and that’s of great credit to their spirit and determination.
“I thought the game was going to be tough, it was.
"Every game we play is going to be a tough fixture. I particularly thought this was going to be our hardest fixture this season so far, obviously, and it proved to be.”
Alexander said his men had to dig out a win from a difficult game.
He added: "We had a fantastic start with a great goal, Ross County grew into the game in the first half and had their opportunities and obviously took one of them.
"In the second half it was about making sure we didn’t give anything stupid and cheap away and try and find that winning goal, which we did.
"Great credit to the players, they stuck at it, worked exceptionally hard for each other and got the rewards for it.
"Ross County are a Premiership team with a proud group of players and manager. They’ve found it tough at the start of the season but they are playing to win points as much as anybody else and they’ve got good quality.
"They showed that in a lot of spells so we had to be at our most diligent to try and keep their opportunities down to a minimum. I think we could have done better in that side of it.
"I would say the two goals we scored were of the highest quality.”
Motherwell had lost 2-1 at home to the same opposition in their final game of last season and Alexander feels Saturday’s reversal of that score shows the progress his team is making.
The boss, speaking to MFC TV, said: “I think the group are making improvements in that side of it. There’s a real investment from them into making the future of Motherwell and their own careers better.
"So there’s a real care there I think for winning games and that I think was the deciding factor in the game.
"I think it was that care to really push for the result.
"We did have some spells of pressure but no real opening chances apart from the one that I felt Tony put away great.
"I’m really pleased with the players and the club today for extending that run.
"We’ve got another tough fixture next week away to Hearts and we’re looking forward to it.
"I think we have to set our own standards of what we expect our performance to be, regardless of who we play against, regardless of where we are in the division.
"Any outside factors should be put to bed and we know how we play well, how we defend well, how we attack well.
"They should be our only barometers going week in week out. We always want to be better and improve.”