Danny Graham and James Hayter exchanged early blows before two goals from Emmanuel Ledesma either side of a Lee Tomlin strike ensured Boro went into the summer dreaming of a promotion charge next season.
Eight of Yeovil's starting line-up for the season finale played in the League One play-off final 12 months ago, but manager Gary Johnson was a notable absentee on the Huish Park touchline as he served a one-match ban following an altercation with match officials during his side's defeat at Charlton last month.
The hosts, who came into the game having won one of their last 12 matches, started brightly and came close when midfielder Sam Foley tested Boro keeper Jason Steele with an early shot.
But Middlesbrough hit back immediately with a snapshot from Graham before the Sunderland loanee spurned a glorious opportunity from four yards following a bright run from Nathaniel Chalobah.
Aitor Karanka's side, who arrived in Somerset having kept 13 clean sheets since Boxing Day, almost paid the price for their slow start when Hayter's lob forced Steele into a good save, but the north east outfit recovered and put the Glovers to the sword.
Boro thrashed Yeovil 4-1 back in October during the first-ever league meeting between the sides and they again highlighted their quality with a three-goal blitz at the end of the first half.
Graham tapped in the game's opener on the half-hour mark after Ledesma's stinging shot was parried by Stech before Ledesma rattled the crossbar and Albert Adomah saw his fierce drive saved.
Yeovil hit back with an equaliser through Hayter after Sam Hoskins' deflected shot fell directly into his path, but Boro retook the lead two minutes later when Graham and teed up Ledesma, with the Argentine making no mistake from close range.
Huish Park was then left stunned as the visitors notched a quick-fire third before the break when Steele's long punt into the Yeovil half was seized upon by striker Tomlin who took the ball around Stech and passed the ball into the empty net.
Boro started the second half as they ended the first and scored a fourth within two minutes of the restart when Ledesma acrobatically volleyed Adam Reach's cross into the bottom corner.
Graham should have added a fifth on the hour mark but, in what will go down as one of the misses of the season, prodded Tomlin's lay off wide from five yards out.
As Yeovil's stay in the Championship came to an unceremonious end, Middlesbrough's elated 1,348 travelling fans were left dreaming in the sunshine of a promotion push next season.