Cameron Jerome scored the only goal of the afternoon as MK Dons progressed into Round Three of the Emirates FA Cup.
Russell Martin's side were in full control of the encounter with substitutes Scott Fraser and Cameron Jerome combining to win the tie and reach the Third Round for the first time in three years.
The Dons will learn their opponents for the tie on Monday evening.
MK Dons made seven changes from the side that drew 2-2 with Shrewsbury Town on Tuesday night.
Stephen Walker, Richard Keogh and Andrew Surman kept their place in the starting XI, while Lee Nicholls was back in goal replacing Andrew Fisher.
Georg Williams, Dean Lewington, Regan Poole, Daniel Harvie sat alongside Keogh in defence while Jordan Houghton, Andrew Surman and John Freeman made up the midfield.
Having scored on Tuesday night, Carlton Morris was rewarded with a start, he partnered Stephen Walker upfront.
The hosts had the first chance of the clash with a minute gone as Mason-Clark’s shot was saved by Nicholls before Lewington cleared the danger.
The Dons first chance of the game came with five-minutes gone, Houghton won MK Dons a corner, Williams met Surman's cross, but his glancing header ended wide of the post.
Keogh was then on hand to prevent Petrasso a chance on goal as he produced a perfectly-timed slide tackle to stop the Canadian in his tracks.
Poole came closest for MK Dons as his strike hit the underside of the bar before Barnet cleared their lines. The right-back gambled on a blocked cross and met the ball inside the area, but was unable to convert.
The Dons continued to dominate possession and once again came close to taking the lead through Walker. Lewington recycled a corner out wide to Keogh, who held possession well before finding the run of Poole. His cross picked out Walker, but he was unable to keep his first-time effort down.
Poole, who was dangerous going forward all afternoon, had the first chance of the second-half - his curling effort was deflected wide for a corner. Sorensen picked out the run of Harvie from the dead ball situation, however, Barnet defending in their numbers to clear.
Barnet then went close through Mason-Clark as the Barnet man attempted an overhead kick from a corner, Keogh was in the right place as he put his head on the line to block the strike.
Morris linked up well with Scott Fraser as he found himself inside the area, the striker shifted onto his right foot before curling narrowly wide of the far post.
Nicholls had to be alert at the other end to deny a quickly taken Barnet free-kick as they tried to catch him off guard.
The Dons dominance was soon rewarded as Cameron Jerome gave Russell Martin's side the lead, after Harvie and Fraser combined well down the left, the latter delivered a low cross for Jerome - he converted with a clever flick across goal. 0-1.
With the game drawing to a close, Loach produced a strong save to keep Barnet in the clash, he got down well to his left to deny Harvie.
Williams then put his body on the line as he blocked Nugent's volley, with the clearance landing at the feet of Morris. The striker drove MK Dons forward before playing inside to Sorensen, the Dane flicked into the path of Jerome, who was unable to keep his effort down.
The Dons professional performance sees them progress into Round Three of the Emirates FA Cup.
MK Dons XI: Nicholls, Williams, Lewington (C), Keogh, Poole, Morris, Walker, Surman (Fraser 66), Harvie, Houghton (Sorensen 13), Freeman (Jerome 66).
Subs: Fisher, Cargill, Gladwin, Kasumu.
Goals: Jerome (82)
Booked: Freeman (12)