Amad led Sunderland's comeback with a stunning goal to impress Erik ten Hag and fire the Wearside closer to the Premier League.
The on-loan Manchester United winger curled home a brilliant 30-yard shot to level the game before Tony Mowbray's men sealed a win through Trai Hume's header. With summer target Jobe Bellingham in the stands ahead of a possible transfer to Wearside from Birmingham inflicted Luton's first defeat in 14 games.
And they extended their own unbeaten run to ten games, ahead of Tuesday's second leg at Kenilworth Road. Amad's best chance of playing for Sunderland next season - an option he is open to - is to fire them to the top flight, a job he has taken on with relish.
At kick-off, it was like the Stadium of Light of old, raucous and reverberating as Mowbray's side walked out to a 'Til The End banner. Even reaching the play-offs was a minor miracle, and here their injury problems were even worse, fielding a back three without recognised centre-backs.
But what they lacked in height they made up for in skill, flow, and spirit in front of 46,060 fans. Functional Luton had trouble getting the ball off Mowbray's men, such was the quality of their play. They used their ball-playing strengths to the full, with Patrick Roberts, Diallo, Alex Pritchard and Jack Clarke all going at Luton with relentless positive play.
Luton were ahead in the 11th minute, exploiting the lack of height in the home defence. The visitors won three headers from a corner kick with Gabe Osho's nod on falling for Alfie Doughty to smash goalward. Anthony Patterson's reflex block fell for Elijah Adebayo to volley home from close range. It was the weakness that any coach would look to exploit, and one Sunderland couldn't answer. Trai Hume saved a second by blocking Adebayo's shot.
But Sunderland never lie down. Amad collected the ball from Alex Pritchard on the right wing, skipped inside and launched a curling shot from 30 yards. It beat Ethan Horvan for pace and placement, for Amad's 14th of the season.
Ten Hag will have another look at the £20million signing from Atalanta when he rejoins United during their pre-season games. These two have played out four consecutive 1-1 draws, but Sunderland pushed for a lead and got it in the 63rd minute.
Remarkably, given they only had one player on the pitch standing over 6ft - Pierre Ekwah - it came from a header. Winger Jack Clarke clipped in a cross from the left wing and Hume flicked a near post header past Horvath.
Have your say! Will Amad be a regular for Manchester United next season? Join the debate in the comments section.
Meanwhile, Dion Charles denied Barnsley a vital first-leg advantage with a second-half equaliser to earn Bolton a 1-1 draw in their League One play-off semi-final. The Northern Ireland international scored his 21st league goal just four minutes after Nicky Cadden threatened to put Barnsley in the driving seat for next Friday's return leg at Oakwell.
The eventual winners will meet Sheffield Wednesday or Peterborough at Wembley for the right to join Plymouth and Ipswich in the Championship next season.
Salford City also took an early lead against Stockport County in League Two 's first semi-final before Bradford City welcome Carlisle United on Sunday.
