The 34th-minute goal came from a long throw-in by Ryan Zoghby. In a mass attempt to clear at the near post, the ball was deflected across goal to where Blair Scoullar was stationed.
At the far post, Scoullar spun in the air to try and volley the ball clear but only made partial contact to send the ball into the roof of his own net.
Since he dropped back into central defence, Scoullar has been a model of consistency, and his partnership with fellow central defender John Chisholm had been one of Tech's stronger combinations.
"Blair was gutted," coach Mike Fridge said. "It was such an unlucky goal to concede, but these things happen in football."
Fridge praised his side's efforts but said it had played better in earlier rounds of the Cup, and in many ways Saturday's was a flat performance.
Yet in the opening minutes Tristan Prattley made a couple of runs up the left wing that had Technical's massed support roaring encouragement.
Although outnumbered in a crowd estimated at 3000, the "maroon army" made its presence felt.
Then it was Bays' defence looking shaky, as Aiden Gwilt was slow to a back-pass and striker Aaron Burgess almost made first contact, then had to hurdle the diving keeper.
But the well-oiled Bays machine - unbeaten this season - settled and started to string passes together as Jeff Campbell, Jack Beguely and Jason McKeown set up little triangles of possession that tested the Technical backline.
Keeper Nick Tarrant was well protected by some robust tackling across the penalty area as Tech defended in depth, but the youngster still had to make a superb full-length dive to deny Beguely.
The battle in midfield became a concern for Fridge as his team challenged for, but rarely collected, second-phase ball, despite the best efforts of Andy Coburn and Sam Jasper.
Up front, Burgess and Ross McKenzie struggled to make any impact as many passes forward were too high, which played to the strengths of giant Solomon Islands international centreback George Suri, who dominated proceedings in the air.
Referee Michael Hester handed out several yellow cards for what looked like ordinary tackles, and possibly took the "cup tie" nature from the game, as Technical tried to lift the tempo.
Fridge remained calm at half-time: "We only need a goal to get back into this match," he told his team.
His players responded, with Coburn barrelling forward and launching shots, then Scoullar making runs from the deep, obviously trying to make amends, which had the crowd on its feet.
In fluid play, Technical failed to press home its advantage, with final passes overhit or intercepted, giving Bays good counter-attacking options.
Another problem for Technical was the poor delivery of passes at free kicks and corners.
With only one goal in it, the tension mounted as full-time approached. Richard Smith and John Lange came off the bench to bolster the attack, Technical forced Bays backwards and generated some high-pressure play that had been lacking until then.
Fridge later said: "We should have been playing like that the whole game. We let them play too much, and should have been more 'in their face'."
"They're a good side and they played some good football, but if I'm honest I don't think they caused us too much trouble in the last third.
"But, at the end of the day, it's about putting the ball in the back of the net, and in the end it was a Tech player that did it for East Coast Bays.
"It was disappointing. But you can build even on disappointment, and those players with good attitude will come back all the stronger and keener to improve next time."
