A Robbie Keane brace took his recent run to eight goals in five league games to keep Spurs' European march on track.
Berbatov and Keane celebrate another virtuoso display up front
The Irishman got the opener after just 12 minutes, tapping in after good work by Dimitar Berbatov, before the latter volleyed the second home from 25 yards.
Mark Viduka headed in to reduce Boro's deficit and Paul Robinson somehow kept Spurs ahead with two magnificent stops.
Keane's second from Lennon's cut-back proved crucial as Spurs hung on despite Emmanuel Pogatetz's consolation header.
It was another barn-storming game involving Tottenham, who now boast a top- flight aggregate of 104 goals (52 for, 52 against) in Premiership games this season.
After a series of near-misses in the cup competitions this season, the Londoners are desperate to secure a top-seven finish to salvage their season.
But there are easier places to go than the Riverside, especially if, like Spurs, you have failed to win there in eight attempts.
However, it quickly became evident that the match would be decided on which front pairing fared the better - and Berbatov and Keane were peerless in the first hour.
The former, fresh from being named in the Premiership team of the year, was the visitors' main tormentor, and he should have opened the scoring when he shot tamely with the goal at his mercy from 20 yards.
Spurs did not have to wait long for the goal, though, and once again Berbatov was the key.
The Bulgarian beat Emmanuel Pogatetz in the air, turned inside the box and laid the ball perfectly to Keane who side-footed home with aplomb.
With both sides guilty of surrendering possession, the match quickly degenerated into a scrappy affair.
Boro were largely toothless in attack in the first half, though Viduka and Yakubu linked up well just before half time when the former rattled the outside of the post with an instinctive effort.
Dimitar Berbatov cracks home the second from 25 yards
But Spurs were comfortable otherwise - so much so that Lee Cattermole was sacrificed just 40 minutes into the match for Adam Johnson as Gareth Southgate attempted to target makeshift left-back Ricardo Rocha.
It mattered little 90 seconds into the second half, though, when Hossam Ghaly - preferred to the out-of-form Aaron Lennon - lobbed to Berbatov, who swivelled and curled in on the volley from 25 yards.
It was a touch of class from the 26-year-old, and Keane should have wrapped things up on the hour when he dinked over Schwarzer but wide from Steed Malbranque's through-ball.
While there were just two goals in it, Boro had a chance - and Viduka almost reduced the deficit when he turned in the box brilliantly and drilled over from the angle.
It was 1-2 minutes later, though, Stewart Downing's switch to the right proving inspired as he crossed for Viduka to head home unmarked.
Suddenly the hosts were full of belief and only a stunning save from Robinson preserved Spurs' lead when he beat away a Viduka effort from point-blank range soon after.
The England number one was again Spurs' saviour 10 minutes from time when he denied a Viduka curler at full stretch, with the visitors living purely on their nerves.
Unbelievably, with Boro enjoying their best spell of the match by a distance, Spurs broke away to seal it, substitute Lennon cutting inside Pogatetz and pulling back for Keane to smash into the roof of the net.
Pogatetz headed in from Downing's corner late on to again make the most of Spurs' frailty on set-pieces, but the visitors held on to mark Martin Jol's 100th Premiership match in charge with a crucial win.
Middlesbrough boss Gareth Southgate:
"The first 45 minutes was very frustrating. We let them play and they punished us.
"However, we finally stirred ourselves after we scored and only an outstanding save from Paul Robinson kept Spurs in front.
"It's a disappointing result and it means our aim, first and foremost, for the rest of the season is to get a point that will ensure our place in the Premiership next season."
Tottenham manager Martin Jol:"We made it very difficult for ourselves once again and Robinson has saved us with some unbelievable saves. But that is why he is Paul Robinson, because he does that.
"We needed a win and, with the way the other results went against us, you could say it was a must-win, so I am pleased tonight.
"Berbatov and Keane both have 21 goals this season, and Jermain Defoe has goals as well, so I am very happy with my strikers. No other club in the country can boast a front three like that I don't think."
Middlesbrough: Schwarzer, Davies (Arca 64), Woodgate, Pogatetz, Taylor, Cattermole (Johnson 40), Boateng, Rochemback, Downing, Viduka, Yakubu (Lee 70).
Subs Not Used: Jones, McMahon.
Goals: Viduka 66, Pogatetz 89.
Tottenham: Robinson, Chimbonda, King, Dawson, Rocha, Ghaly (Lennon 72), Zokora, Jenas, Malbranque, Berbatov, Keane.
Subs Not Used: Cerny, Defoe, Huddlestone, Ifil.
Goals: Keane 12, Berbatov 47, Keane 83.
Ref: L Mason (Lancashire).