Smith's (centre) fourth of the season saw off Boro
Alan Smith's second half goal was enough for Leeds United to move above Chelsea and finish in fifth place.
With a Uefa Cup place already assured, the win was worth £440,000 to the Elland Road club, as they climbed one place in the league table.
And it kept up their record of not finishing outside the top five in the Premiership for the past four seasons.
Steve McClaren's side had two great chances to equalise towards the end but neither Noel Whelan nor Szilard Nemeth could take advantage.
Smith's goal, after 63 minutes, divided the two teams and was just reward for manager David O'Leary in his 150th game in charge of Leeds.
Irish striker Robbie Keane had the first chance of the match after only three minutes.
Club and country colleague Ian Harte played the diminutive striker in but one-on-one with Mark Schwarzer, Keane could not find the target.
But both goalkeepers were relative spectators for most of the half with the home side pressing forward without a significant cutting edge.
Leeds' only ever present player this season, England keeper Nigel Martyn, did not have one save to make throughout the first 45 minutes.
But United were also far too fancy in their build-up play and never really threatened Schwarzer's goal.
However, towards the end of the half, O'Leary's side started to assert their superiority.
Lee Bowyer had two great opportunities to break the stalemate within a minute.
His first effort drifted wide after he was set up by Harry Kewell, while a minute later he drilled a shot over the bar following a right-wing cross from Gary Kelly.
It was McClaren's men who started the second half the better though.
England's Gareth Southgate and Boro's former Leeds striker Whelan both threatened the home goal.
But it was Leeds who forged ahead after 64 minutes.
A superb overhead pass from Keane was latched onto by his striking partner Alan Smith. The England Under-21 forward coolly controlled the ball on his chest while the Boro defence looked on.
Smith thundered the ball past Schwarzer with the outside of his right foot for only his fourth Premiership goal of the season.
Moments later Keane lashed into the side-netting from an acute angle before Whelan whistled a fine volley over Martyn's crossbar.
Whelan prodded his forward partner Nemeth clear of the home defence after 75 minutes.
Nemeth shot straight at Martyn when well-placed and the England keeper recovered to avert any danger and keep his cleansheet intact.
The result meant that Boro finished the season as they had started it with four successive Premiership defeats.
Leeds: Martyn, Kelly, Ferdinand, Matteo, Harte, Bowyer, Bakke,
Johnson, Kewell (Wilcox 90), Keane, Smith.
Subs Not Used: Robinson, McPhail, Duberry, Batty.
Booked: Matteo, Martyn.
Middlesbrough: Schwarzer, Stockdale, Ehiogu, Southgate,
Cooper (Murphy 84), Greening (Debeve 76), Ince, Mustoe,
Downing (Windass 66), Whelan, Nemeth.
Subs Not Used: Crossley, Johnston.
Attendance: 40,218
Referee: U Rennie (Sheffield).