Ex-Shrewsbury Town defender Tierney celebrated his first goal in a Colchester shirt by heading home what proved to be the winner after 17 minutes.
It was only the second goal of his career following his first, last season while at Shrewsbury.
He actually started the move that led to the goal by embarking on a powerful run into the heart of Stockport's defence.
His pass was helped into the path of Kemal Izzet by David Perkins and the final cross from Izzet was headed gleefully home by Tierney, who continued his run into the box.
The ball cannoned into the net off the underside of the bar.
Play-off chasing Stockport rarely looked like fashioning an equaliser, apart from for one ceffort on 20 minutes, just three minutes after Tierney's deadlock breaker.
In fact, it looked a goal all the way as Johnny Mullins met a corner with a thumping header from close range.
However, home keeper Jimmy Walker pulled off a sensational save, instinctively clawing the ball to safety.
Colchester had chances to add to their lead with both wingers Simon Hackney and Mark Yeates very prominent, specially in the first half.
Yeates peppered the target with a couple of shots and a header, while Hackney, who was making his full debut since his switch from Carlisle, delivered a string of good crosses into the box.
Man-of-the-match Izzet squandered a couple of chances, one in either half, but in the end it didn't matter as the U's advanced into 11th spot to keep their faint play-off hopes alive.
It was a bad night all round for Stockport. News broke before kick-off that their manager Jim Gannon had been given permission by his chairman to speak to Brighton about the vacant managerial post on the Sussex coast.
This defeat at Colchester therefore looks like being Gannon's final match in charge of County.