Tom Corner cancelled out Wright's opener before an outrageous free-kick in the dying embers from the aforementioned sent Albion home empty handed when a draw may have been a fair result.
Michael Morton came into his first competitive game in charge of Tadcaster without the likes of Danny Frost, Sam Akeroyd, Corey Roper and Jason Mycoe.
Morton did however give new signing Cam Murray a start along with midfielder Jake Ellam.
It wasn’t the best of starts for Albion though as the home side broke the deadlock with the season just seven minutes old.
A ball in behind Aaron Hardy looked to have been retrieved by the former Huddersfield Town defender but Jerome Wright persevered, ran out with the ball and slotted into the back of the net.
Taddy had a decent chance of their own to draw level four minutes later when Andy Milne set Aiden Savory away in behind Rammy’s back-line but the former Farsley man couldn’t find the target.
The Brewers certainly grew into the contest and kept the ball better as the half went on but there wasn’t much between the two teams with few clear cut openings.
Having said that, Rammy spurned a glorious chance to double their lead in the 34th minute. Appeals for a high boot were waved away and as the protests continued Tom Brooks dragged wide of the goal from close range.
After a high number of niggly fouls and soft free-kicks Albion did in fact level proceedings five minutes from the break.
Conor Sellars’ deep curling free-kick was nodded down by Andy Milne and poked into the net by Tom Corner to open his account for the campaign.
Half-Time: Ramsbottom United 1-1 Taddy
With the sun continuing to shine down on the Harry Williams Stadium Taddy came out in the second forty five and were gifted an opportunity to take the lead shortly after the restart.
A loose header back by a United defender allowed Savory in behind and he did well to control and get his shot off whilst being under pressure but Martin Fearon thwarted the effort.
Both sides couldn’t be separated at this point with all battling hard to gain a foothold. Chances began to fall at both ends and Greg Daniels tried his luck twice in two minutes after the hour mark.
First of all the number 10 curled harmlessly over the bar before secondly doing well to get his shot off in the area without troubling Ingham.
Substitute Josh Greening came off the bench in the hope of producing that bit of magic required and he had a good chance to do so twelve minutes from time but he couldn’t generate enough venom on the shot to test the Rammy goalkeeper.
But there was to be an elusive third goal and it was the home side that scored it with five minutes to go.
Jerome Wright stood over a free-kick five yards in from the right-hand touchline and any normal player would simply curl it in or hang it up towards the back-post, but not Wright.
The former FC United of Manchester man whipped a stunning free-kick over the wall and in off the post catching Ingham out.
As Taddy pushed for an equaliser in stoppage time, Ramsbottom were reduced to ten men as Max Hazeldine caught Ingham late and was shown a second yellow card.
There was to be no late equaliser for the Brewers at Rammy this season but there were still plenty of positives to take into Tuesday night’s home opener against Ossett Albion.
Full-Time: Ramsbottom United 2-1 Taddy
Ramsbottom: Fearon, Heathcote, Brownhill, Stott ©, Thompson, Roscoe, Brooks (Williams 81), Pierce (Moran 74), Gaskell (Hazeldine 63), Daniels, Wright
Unused: Meaney, Rother
Tadcaster: Ingham, Hardy (Grant 73), Howarth, Davidson, Milne ©, Barrett, Murray (Greening 66), Ellam, Corner, Savory, Sellars (Dixon 84)
Unused: Crouz, Shepherd