The visitors edged the first half and came closest to breaking the deadlock when Astley Mulholland sent the crossbar shaking.
Taddy however sparked into life in the second half as Savory opened the scoring thirty seconds after the restart before rifling home a second in the dying embers.
The Seagulls did pull one back deep into stoppage time courtesy of Gareth Grant but it wasn’t enough to stop Tadcaster extending their unbeaten run to seven matches.
After having to deal with a ten-day break thanks to the ‘Beast From The East’, it was a brilliant opportunity for either side to climb up into sixth place in the Evo-Stik North Division.
Unsurprisingly Albion boss Michael Morton named an unchanged team for a fourth successive league outing as midfielder Pete Davidson shrugged off a knock.
Casey Stewart, who has solidified his place in the side after a string of impressive performances, had the first effort at goal chopping inside and out before clipping tamely into the hands of goalkeeper Matt Cooper.
The side from North Wales started the brighter though and they almost took the lead inside fifteen minutes but were denied by the woodwork.
Talisman Astley Mulholland jinked inside from the left-wing who’s quick change of direction saw defender Fraser Papprill lose his footing but the Bay striker struck venomously off the face of the crossbar.
The flow of the first half was similar to the Brewers’ most recent match against Droylsden as the away side were enjoying longer spells in possession and in dangerous territory without creating a great deal in the final third.
Neither side were yet to get out of first gear but it was Alan Morgan’s side who continued to look the most likely to score the opening goal as left wing-back Louis Barnes struck a blistering swirling shot from 27 yards which was pushed clear by Michael Ingham.
The former York City number one was called into action again seconds later when he had to get down well to gobble up Elliot Rokka’s low drive.
Billy Whitehouse, who has been another fantastic addition into the Taddy team, did well to manufacture an overhead kick on target but it was never troubling Cooper in the Colwyn goal.
After a first half with both teams tentatively feeling each other out, it was all change in the second half as whatever bosses Michael Morton and Simon Collins said at the interval, it had an immediate impact.
Corey Roper, who was excelling in the centre of midfield with Pete Davidson and Chris Howarth, swept out to Harry Sheppeard whose curling ball down the line created a one v one situation between Whitehouse and Barnes.
The winger, who was in Leeds United’s first-team as recently as January last year, saw his cross deflect off of Barnes spiralling high up in the air and into the box to which Aiden Savory superbly flicked over his head with his left-foot.
The striker never took his eyes off the flight of the ball and executed the difficult technique perfectly to find the bottom corner.
The former Farsley man who played as a centre back for all of last season, had a glorious chance to double his and Taddy’s tally three minutes later.
Aaron Hardy surged into the centre circle and clipped a perfectly weighted ball in behind setting Albion’s number ten away but he struck the bouncing ball wide of the mark.
Taddy were firing on all cylinders at this point and they came agonisingly close to extending their lead on 55 minutes.
Whitehouse’s clever scoop in behind Bay’s back-line set Casey Stewart in on goal down the right-hand side and his close-range strike thumped off the inside of the post.
Danny Andrews had a rare sighting at Taddy’s goal shortly after the hour mark as he couldn’t scramble past Ingham after trapping the ball between his legs in the six-yard box.
Nevertheless the Brewers were all over their Welsh opponents in the second half and they deserved to be further in front as another clear-cut chance was squandered.
Savory couldn’t turn Stewart’s low cross goalwards but it did ricochet kindly into the path of Billy Whitehouse whose powerful shot from nine yards was well saved by Matt Cooper.
Whitehouse was involved heavily in Albion’s attacking play and he looked certain to score when Savory cutely flicked in behind two minutes later but the wide-man could only curl over the bar.
Both sides were certainly making up for the lack of chances in the first forty five as it was Bay’s turn to pass up on a gilt-edged opportunity.
Kyle Jacobs’ dangerous free-kick was met by an unmarked Billy Sass Davies but the man on loan from Crewe Alexandra couldn’t direct his header on target.
With the clock approaching the final ten minutes and still only one goal separating the two play-off contenders, midfielder maestro Pete Davidson went close as his dipping left-footed strike from distance dropped narrowly over.
However, with three minutes remaining of the normal time, Taddy did score a deserved second goal to wrap up the victory.
Fraser Papprill’s drilled clearance ran invitingly for Aiden Savory who was simply too quick, strong and powerful for Sass Davies putting the defender on the floor before composing himself and striking superbly into the far corner, again with his weaker left-foot.
There was to be one final twist in the England v Wales encounter though as the visitors did pull one back deep into injury time thanks to Gareth Grant escaping his man on a corner and towering a header home.
But it was too little too late for the Seagulls who did end Taddy’s recent run of consecutive clean sheets but couldn’t stop them extending their unbeaten run to seven.
Full-Time: Tadcaster Albion 2-1 Colwyn Bay
Tadcaster: Ingham©, Sheppeard, Hardy, Roper, Papprill, Barrett, Howarth, Davidson (Langton 90), Stewart (Sellars 90), Savory, Whitehouse
Subs unused: Lock, Mycoe, Pugh
Colwyn Bay: Cooper, Jacobs, Barnes, Sass Davies, Grant, Barnes© (Hindle 62), Andrews, Booth (Rainford 84), Rokka, Mulholland, Mendes
Subs unused: Leigh, Brizell, Horrocks
Attendance: 192
Referee: Luke Watson