Cole scored in each half – the first a penalty – with Chris Long wrapping things up against a Livi side whose lone strike came from Jack Fitzwater, meaning ninth placed ’Well move onto 35 points from 32 games which is nine points clear of second bottom Hamilton and 10 ahead of bottom club Kilmarnock.
Alexander said: "I don’t think there is a secret (with Devante’s good form). Look, he’s a good player.
"He’s a good striker. I think we’ve got other good strikers and other good players in the squad but – I think I said yesterday – we always have a way of treating people, that’s across the board.
"And I think he’s responded well to it. I don’t know how he’s been treated in the past, I can’t really put my finger on it.
"But we ask him to play in good areas and we try to feed these lads because we know they’re goalscorers. Chris Long’s got a fantastic goal as well today, Jordan (Roberts) scored last week and was such a threat.
"So we know we’ve got good talented players but we try to keep round pegs in round holes and I think Coley’s an out and out striker.
“I thought we started the game in a real good tempo, pinned Livi in for long periods of the game and deservedly took the lead.
"They had a good spell just before half-time when they were sniffing an equaliser and it was a good warning for us going into half-time that the game wasn’t dead.
"We scored the second goal, unfortunately conceded quite soon after to make it difficult for ourselves but I thought we gradually gained control again and once we got the third I thought we were reasonably safe but it was only because of the way we approached the game. I’m delighted for the players.”
Motherwell dominated the early stages with away keeper Robbie McCrorie saving from Jordan Roberts and Stephen O'Donnell before a strong penalty shout was denied as Tony Watt went down under a challenge by Aaron Taylor-Sinclair.
A fine run from Watt on seven minutes then set him up for a shot which went wide of the right post.
On 14 minutes a poor clearance by McCrorie was collected by Cole who drove forward before shooting wide at the near post.
There was a blow for the hosts nine minutes later when Watt went off injured amd was replaced by Chris Long.
But there was joy for the claret and amber team just after the half hour when Cole comfortably slotted in a penalty awarded for Matej Poplatnik's clear foul on Robbie Crawford.
Stephen O'Donnell's outswinging free-kick from the right flank on 39 minutes struck Lamie in the centre but the ball went comfortably through to McCrorie.
Home keeper Liam Kelly then made a brilliant stop when he went down smartly on 40 minutes to save a Poplatnik header following a long throw into the box.
The last action of the first half saw a nervy moment for the hosts as Josh Mullin's 20-yard free-kick was an excellent effort but it hit the bar on the way over.