The Saints have suffered with travel sickness this season but their first away win could prove vital to their survival hopes.
Boro, who once had hopes of a Champions League place have had a disastrous league run since the turn of the year.
They can be thankful for an impressive first half of the season because three points from their last ten games is relegation form.
Southampton were full value for the win. They retained a good shape for 90 minutes and Middlesbrough struggled for a breakthrough.
In addition the Saints had a matchwinner in Peter Crouch. With two brilliant goals the lanky striker is now the club's leading scorer for the season.
Southampton showed a positive approach from the start and were rewarded with a goal after 14 minutes from Andreas Jakobsson. When Henri Camara passed across the face of the goal Jakobsson had an easy scoring chance at the far post.
Middlesbrough's defence did not look solid against the visitors' attacks, but the home side levelled up before half-time.
When a Boudewijn Zenden shot bounced off Antti Niemi, Joseph-Desire Job crossed the ball to Jimmy Floyd Hasselbaink who had an easy close-range task for his 14th goal of the season.
The Saints regained their lead after 59 minutes when Crouch left Mark Schwarzer helpless with a perfect header from Olivier Bernard's left-wing cross.
Middlesbrough snatched a point at Southampton earlier in the season with a late two-goal fightback, but Crouch crushed any hopes of a repeat performance, putting the match beyond doubt in the 67th minute.
Middlesbrough suffered their usual fate after playing in Europe, but Southampton were in celebration mood at the final whistle.
"The Saints are staying up, now you are going to believe us" chanted their fans.