Goals from Josh Morris, Kevin Van Veen and Sam Mantom put the game beyond Chesterfield, who were all too often out muscled by their visitors.
Alexander lauded his playing staff, who responded perfectly to a midweek defeat: “The players were brilliant, they committed to the game.
“We spoke a couple of times about the game on Tuesday and what it takes to perform at our level. It takes belief in how good you are and they showed that today.
“They were composed, they were committed to every action and that’s what it takes to come away and win like that.”
The game was still in the balance at the break, but Morris’ goal three minutes into the second half seemed to take all the wind out of the Spireites’ sails.
Alexander said: “When you’re on top you hope for that goal to give you the breakthrough but sometimes you have to be patient.
“It’s not easy coming to Chesterfield or any club in this division. You have to earn that right and we did that.
“Once we got that goal we didn’t get any better we just continued with what we were producing.
“It was great to watch.
“To win 3-0 away is great testament to the players.”
It wasn’t just the way Scunthorpe attacked that pleased their manager, it was the way they battled all over the pitch.
He added: “We just continued to keep the foot to the floor and produce an all round performance, defensively really strong and aggressive and our attacking energy and interplay was superb to watch.”