At the end of a tense first-half in which Boro could have had a penalty, Georginio Wijnaldum powered the breakthrough goal past Brad Guzan in stoppage time to settle the nerves.
The Reds doubled their advantage just five minutes into the second-half through Philippe Coutinho's 25-yard free-kick before Adam Lallana added a third to put the game out of sight.
As a result of Manchester City's thrashing of Watford, Jürgen Klopp's side finish fourth and will face a two-legged qualifier to reach the Champions League group stages in August.
It is just the second time in eight seasons that Liverpool have finished in the top-four while their final points total of 76 is one they have only matched, or bettered, four times in the Premier League era.
Boro return to the Championship next season having finished 19th in their return to the top-flight, accruing just 28 points and having scored a league-low 27 goals in 38 games.
Wijnaldum pile-driver puts hosts ahead after Reds escape penalty scare
Klopp made just one change to the Liverpool team that thrashed West Ham United last weekend with Roberto Firmino returning from a muscle injury to replace Divock Origi.
Visitors Boro dropped top goalscorer Álvaro Negredo to the bench as Steve Agnew favoured the height of Rudy Gestede up-front, while Grant Leadbitter replaced Marten de Roon in midfield.
As expected Liverpool saw almost all of the possession from the off and Firmino's effort inside 20 seconds - albeit an easy save for Boro goalkeeper Guzan - displayed their intent.
Before five minutes had passed Nathaniel Clyne had a decent opportunity to properly test Guzan but he dragged his low drive wide after James Milner's cross had been flicked into his path.
Liverpool soon dropped down to fifth as Arsenal took the lead at home to their Merseyside neighbours and that added to the palpable tensions inside Anfield, Boro's stubborn back-line holding firm.
Guzan remained untroubled as Liverpool failed to carve open clear chances, Emre Can firing just wide of the post after an opening at the edge of the box.
Reds follow up opener with two quick-fire goals before the hour mark
And there were huge sighs of relief among the home supporters on 22 minutes when Martin Atkinson decided against awarding a penalty as Patrick Bamford went down under contact from Dejan Lovren.
Nervousness seeped into Liverpool's play as they laboured to open up gaps in Boro's defence and their shoot-on-sight tactics yielded no reward, Sturridge going close as he curled just past the post.
But just seconds before the break, a nicely-knit move down the right saw Firmino flick into Wijnaldum's path and the Dutch midfielder's thunderous right-footed strike flew past Guzan at his near post at the Kop end.
That finally gave Liverpool their much-desired lead and sent Anfield into raptures, seemingly paving the way for a less tense second-half.
And so it proved immediately, as the Merseyside outfit moved another step closer to hearing the iconic Champions League anthem at Anfield again on 50 minutes.
After Daniel Sturridge had been fouled around 30 yards from goal, Coutinho stepped up to the free-kick to curl over the wall and beyond Guzan into the bottom left corner for his 13th of the season.
Elated Anfield start to enjoy unusually comfortable season finale
Liverpool had their breathing space and with Boro on the back foot, the hosts looked to run rampant. George Friend blocked Firmino's chested volley inside the area, but it wasn't long until Liverpool made it 3-0 shortly before the hour mark.
Lallana led a quick counter-attack from a Boro corner but the England midfielder looked to have brought it to a premature end when his attempt cross was met by Fabio.
But Lallana himself won the second ball, allowing it to drop for Wijnaldum to return it to his team-mate to side-foot a composed finish into the bottom corner for his first Liverpool goal since the last meeting between these two teams back in December.
Boro almost summoned an immediate response when Simon Mignolet did well to deny boyhood Liverpool fan Adam Forshaw one-on-one, but from there the home side were thoroughly comfortable.
Guzan denied Coutinho a second before Sturridge curled wide as the game became a procession, substitute Lucas Leiva's every touch - in this potentially his farewell appearance for the club - greeted by cries of "shoot!" from the Kop.
The party atmosphere coupled Liverpool's fourth successive clean sheet but most importantly ensured a return to Europe's premier club competition - pipping Arsenal to fourth by a single point.