First-half goals from Mido, Jeremie Aliadiere and Didier Digard on his first start for the club ensured the Teessiders avoided falling victim to a side with a proud giant-killing tradition.
Marvin Emnes was also on the mark after the break on his Boro debut, before Adam Johnson's curling effort wrapped up a comprehensive victory for the Premier League club.
Boro boss Gareth Southgate handed a first start to £3million full-back Justin Hoyte, while Mido was restored to the starting line-up after his impressive opening to the new season.
It took the Egypt striker just 11 minutes to fire his side ahead following a strong start from Boro which saw Johnson twice test visiting keeper Josh Wagenaar in the opening minutes.
Mido raced onto a long ball that bounced over the head of the defence and held off Lee Peltier before picking his spot beyond a helpless Wagenaar from ten yards.
Digard then doubled the advantage on 22 minutes with a superb 30-yard strike.
The former Paris St Germain starlet took the ball off Kieran Murtagh in midfield before racing towards goal and unleashing a powerful drive that Wagenaar was unable to keep out despite getting his hands to the ball.
Middlesbrough were cruising and Aliadiere could have made it 3-0 just minutes later when he curled an effort from distance just over the crossbar.
But the French striker was not to be denied as he put his name on the scoresheet after 32 minutes when he cut in from the right flank and picked his spot to Wagenaar's left.
To Yeovil's credit they refused to throw in the towel and Gavin Tomlin reduced the arrears on the stroke of half-time.
Just moments after drawing a save out of Ross Turnbull, the Town striker tucked the ball home from close-range after taking advantage of slack marking to bury a free-kick from the left.
But a ruthless Boro snuffed out any hopes of a fightback within two minutes of the restart when Emnes claimed his side's fourth of the night.
The Netherlands midfielder headed home Hoyte's pinpoint cross from the right to effectively kill off the game.
Boro continued to look comfortable during the remainder of the second half with Mido finding the side-netting and Johnson again testing the agile Wagenaar with a low drive.
Johnson was finally rewarded for his attacking endeavour when he curled home the goal of the night on 66 minutes.
The tricky left winger picked out the top corner from the edge of the penalty area to complete the scoring and further his reputation as another star in the making from the club's youth productive academy.