Tottenham, playing on the ground which has been their temporary home all season, got off to a dream start when Dele Alli scored from close range but Alexis Sanchez equalised with a header and Ander Herrera fired United's victor midway through the second half.
For both sides, the FA Cup remains their sole hope of winning any silverware this season and they are unlikely to settle for scraps on Saturday night.
Spurs led after 11 seconds of their Premier League win over United at Wembley in January, and they needed only 11 minutes to go 1-0 up on this occasion.
Davinson Sanchez aimed a long, hopeful ball down the right flank, catching Ashley Young horribly out of position and Pogba off guard.
Jose Mourinho's side survived the siege and levelled on 24 minutes, Wembley specialist Alexis Sanchez rising to direct an athletic header across Spurs keeper Michel Vorm from Paul Pogba's ideal cross for his eighth goal in eight appearances at the stadium, BBC reports.
Tottenham hit the post through Eric Dier in first-half stoppage time but United held off Spurs' challenge with relative ease after Herrera's goal.
"In the second half, good brains and good organisation - very confident and calm, very much in control even when Spurs had the ball".
Mourinho's side threatened to move two goals clear, with Vorm saving well from Pogba and Lukaku, before dropping deep to keep Spurs frustrated in the closing minutes and send the travelling fans into raptures at the final whistle.More news: Philadelphia Police Release Audio Of Starbucks Incident
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"To win a trophy when you face a side like Manchester United, Chelsea or Manchester City is not easy".
"And it will be a fourth final in three years".
Spurs will likely seal their place in the Champions League for a third successive season in the coming weeks as Pochettino's proof that progress is being made.
Ander Herrera has Manchester United dreaming of FA Cup glory after Mauricio Pochettino's Tottenham again suffered semi-final sorrow.
United recovered from going a goal down to beat Tottenham 2-1, with Alexis Sanchez and Ander Herrera scoring for the Red Devils. It was the most hard when we started the season.
Christian Eriksen has had a hand in 10 goals in his last six FA Cup appearances for Spurs (3 goals, 7 assists).
Jose Mourinho has reached his sixth major domestic final in England (2 FA Cup, 4 League Cup), winning each of his previous five.