Cook's expertise helped Bradford to a 3-1 lead in the first half, as an Elliot List strike shortened the deficit early in the first half, before Canavan netted late on.
Bradford have now clinched their second straight victory, whilst Stevenage suffer their first defeat of the league campaign.
The home side opted to make just the one change from Saturday's victory over Oldham, as Charles Vernam replaced Gareth Evans.
Bradford City: O'Donnell; Cousin-Dawson, O'Connor, Canavan, Ridehalgh, Watt, Cooke, Gilliead, Vernam, Angol, Cook
Stevenage: Anang; Wildin, Cuthbert, Vancooten, Coker, Taylor, Lines, Reeves, List, Norris, Carter
Story of the match
The Bantams needed an early goal to get the Utilita Energy Stadium rocking and to blemish Stevenage's run of clean sheets, and that's exactly what they did.
A quick start to the game prevailed as former Tranmere Rovers team-mates Liam Ridehalgh and Cook linked up, with the left-back surging down the wing before lofting a cross to the back post, where Cook waited, before nodding the ball past a helpless Joseph Anang.
Stevenage had had such a good start to the league for a reason however, and nearly immediately struck an equaliser. Ben Coker found space on the left-wing and crossed deep to find Boro's talisman Luke Norris, but his close range header was smothered by Richard O'Donnell.
Adams' Bradford looked to double their lead in less than five minutes, as a long ball found Saturday's hero Lee Angol on the wing, who cut inside but could only rustle the side netting.
But there missed chances were punished seventeen minutes in, as Stevenage nabbed their equaliser. An inswinging cross from the right was knocked down by Norris into the path of List, and the former Gillingham winger made no mistake in rifling his half-volley past O'Donnell.
The Bantams were eager for a quick response courtesy of Alex Gilliead, as the winger twice created opportunies for himself, with the first being dragged wide and the second being dealt with comfortably by Anang.
However, a hectic two minutes for Bradford saw Adams' side miss a penalty, and to then score an outstanding goal just a minute later. Vernam and Cooke linked up brilliantly on a swift counter-attack, as Vernam was ruthlessly dragged down by Luther Wildin.
Up stepped Angol, who had done the business on Saturday, but the forward failed to convert on this occasion, as Anang parried his effort in confident fashion. The rebound was briefly cleared, but Cooke was influential once again, as the midfielder made himself some space and crossed to the back post, where Cook waited and confidently volleyed into the bottom corner.
But as if his first half hadn't been good enough, Cook added to the scoreline, netting his third. In what had seemed to be a difficult position, as Cook controlled the ball between two Stevenage defenders before muscling his way past both, the striker surged through on goal before delicately dinking over the stranded Anang, grabbing a perfect hattrick and his first three goals of the season.
Heading into the second half, and it would take almost eighteen minutes before the first chance of note would happen. Cook was once again the threat, as a towering cross is nodded on by the forward, but Anang blocked his effort.
The Bantams would go onto dominate the second half, but created very little chances to show for it. Adams looked to change this, granting Caolan Lavery and Yann Songo'o debuts.
But as the game neared its end, captain Canavan played his part, getting in on the action. Some clever footwork on the touchline saw Lavery weev his way past a challenge, before floating the ball towards Canavan, who comfortably hammered the ball into the back of the net.
As the referee put the whistle to his mouth it was quite the performance from Bradford, showing why they are backed by so many as potential title candidates.
Vintage Bantams performance
Despite losing the clean sheet, Bradford fans can have no complaints about tonight's affair, with the Bantams producing a vintage display against a confidence looking Stevenage side.
Bradford looked in control from the first minute, dominating possession and playing some nice football which got the fans off of their seats numerous times. Every player simply did job tonight.
How will Stevenage respond?
A first defeat of the season is always a kick in teeth, but Revell needs to ensure that his side's heads do not drop and that confidence remains high in the Stevenage camp.
If you look at how the Boro have performed so far this campaign, then you'll know this was a very un-Stevenage like performance. Revell's side have oozed quality and confidence which stems from their defensive stability, so when that crumbled in the first half, Stevenage never looked like coming back. Now it all depends on how they respond on Saturday against Port Vale.
This doesn't need much explanation, but a perfect first-half hattrick and an outstanding lone striker performance showed the true quality of Cook today.
Cooke and Vernam were both also fantastic, looking dangerous when spearheading the attacks.