Boro arrived at Glanford Park with the worst away record in the Football League, but two first-half goals sealed a second successive victory following Saturday's win over Crystal Palace.
Kris Boyd put Mowbray's men in control inside the opening 10 minutes with a simple finish at the far post for his fifth of the season and Scott McDonald curled in the second with 23 minutes gone.
It could have been a different story had Scunthorpe taken one of three excellent chances in the latter stages of the first period, but the Iron came up against an inspired Jason Steele in the Boro goal.
And Boro held on for a victory which saw them move out of the relegation zone, while Scunthorpe were left to reflect on their fifth home defeat of the season.
Having endured such a miserable campaign on road coming into the game, the visitors could not have wished for a better start as they led inside six minutes.
A sweeping move across the field saw the ball with Joe Bennett and he advanced past Cliff Byrne and whipped in a low cross which left Boyd with the simplest of tap-ins at the far post.
It was Boro's first attack of the match and just their third away goal of the season.
Mowbray's men were buoyed by their impressive start and midway through the first half McDonald gave his side an elusive two-goal advantage.
Boyd held the ball up well and laid it off to the former Celtic midfielder and curled his shot in off the post from 22 yards.
Scunthorpe were shell-shocked by the start but they finally tested Steele just before the half-hour mark when Josh Wright's stinging drive saw the Boro keeper tip over well.
And soon after Steele produced an even better stop to protect his side's two-goal lead when his flying save deflected Chris Dagnall's powerful drive from distance over the bar.
The hosts were building up a head of steam and should have reduced their arrears but Dagnall could not direct his header goalwards from eight yards.
And Boro were again lucky to go into break without conceding when Steele produced another fine save to beat away Michael Raynes' volley.
The interval came at bad time for Scunthorpe as they ended the first period in command, but they continued to create chances after the break.
First Dagnall glanced a header wide after a good cross from Freddie Sears and then Byrne could not keep his header down at the far post.
Boro picked up though and Joe Murphy was forced into his first real save of the game on the hour mark. David Wheater latched onto Tony McMahon's long ball and stabbed a low effort which Murphy kept out with his legs.
Scunthorpe hustled and bustled in the final 20 minutes as they desperately searched for a way back into the game but they came up against a Boro defence in no mood to give anything away, with Kevin McDonald's 25-yard effort glancing off the outside of the post their best effort.