Boyd, who was linked with a move away from the Riverside Stadium in the transfer window, opened the scoring in the eighth minute when he latched onto a hopeful ball forward from Seb Hines before coolly lobbing Josh Lillis.
The hosts spurned several chances to extend their advantage but grabbed a second in the 69th minute as Tony McMahon's left-wing free-kick sailed into the far corner.
McMahon's strike came seven minutes after a bizarre incident that saw referee Rob Lewis award Middlesbrough a penalty, only to change his mind following consultation with one of his assistants.
Lewis took centre stage again with 16 minutes remaining as he dismissed Scunthorpe midfielder Abdi Ibrahim for a second bookable offence.
The Iron have now lost nine of their last 11 Championship fixtures and remain 23rd, but things are finally starting to look up for Boro, who are unbeaten in six league games.
Julio Arca and Marvin Emnes returned to the Middlesbrough team in place of Barry Robson (ankle) and Gary O'Neil, who was sold to West Ham last week. New signing Maxi Haas was named among the substitutes.
Joe Garner made his Scunthorpe debut following his loan move from Nottingham Forest, but fellow forward Lee Miller was denied permission to face his parent club. Michael Nelson was also unavailable as he did not sign in time to play in the fixture.
It was the visitors who threatened first in the seventh minute as Eddie Nolan headed straight at Jason Steele from Mark Duffy's free-kick.
However, Boro went in front moments later as Boyd pounced on some slack defending to notch his sixth league goal of the season.
Boyd and Hines spurned further chances and Bobby Grant headed wide for the Iron before the game sprung into life in the latter stages of the first half.
Andrew Taylor's excellent low cross provided Leroy Lita with a golden opportunity to double Boro's lead in the 34th minute, only for the striker to miss the target with a sliding effort from inside the six-yard box.
Scunthorpe's Mark Duffy then curled a 30-yard free-kick narrowly wide of the top-left corner, but the hosts were quickly back on the attack, with Joe Bennett firing over following good work from Emnes and Arca testing Lillis from the edge of the area.
The hosts also saw a penalty appeal rejected shortly before half-time when the ball appeared to strike Andrew Wright on the arm.
Tony Mowbray's men continued to push forward after the interval and Lillis was relieved to see an Arca free-kick drift wide of his right-hand post.
Boro were awarded a spot-kick in the 62nd minute as Lita tumbled under pressure from Wright, but referee Lewis duly reversed his decision to the fury of the home crowd.
The controversy was soon forgotten as McMahon found the far corner with an inswinging free-kick from the left.
Ibrahim then picked up a second yellow card for a foul on the impressive Emnes as Scunthorpe's evening went from bad to worse.