The former Millwall midfielder, who completed his move to Ewood Park earlier this month, planted a precise header into the top corner on 93 minutes to secure a share of the spoils.
A stunning Brett Ormerod strike on 16 minutes looked to be the difference between the two sides in the North Wales sunshine.
Rovers came up against a goalkeeper in inspired form, as Andy Coughlin made superb saves to deny trialist Yann Songo'o and Alan Judge in the first half.
Gary Bowyer's side were also twice denied by the woodwork, as last season's top scorer Jordan Rhodes struck the stanchion and John O'Sullivan hit the post.
But deep into added time, Taylor came to Rovers' rescue, as he headed home David Dunn's cross.
The game served its pupose as a useful fitness exercise for the Rovers stars, who only returned for pre-season training nine days ago, with 21 players getting 45 minutes of football under their belts.
New boss Bowyer named a strong starting line-up for the game. Rhodes and Leon Best started in attack, with returning Rover Judge supporting from midfield.
Young Spaniard Hugo Fernandez was handed his first taste of senior action, whilst trialist Songo'o, a Cameroon youth international, partnered Grant Hanley at the heart of the defence.
Jake Kean, who missed the end of the 2012-13 season after undergoing an operation on a knee injury, made a welcome return in goal.
After a scrappy start, the first chance of the game fell to the home side. The lively Kevin Thornton slipped a clever ball in behind the Rovers defence to Bradley Reid, whose shot was saved by Kean at his near post.
Rovers came close to breaking the deadlock on 10 minutes. Following a foul on Best right on the edge of the box, Morten Gamst Pedersen fired in a free-kick, hard and low, which forced a smart save from the Wrexham keeper.
Neat interplay by Wrexham did lead to the opening goal six minutes later. Ormerod was afforded too much time and space to shoot and he fired an unstoppable 20-yard shot into the top right-hand corner of Kean's goal.
Rovers almost hit straight back, but Pedersen's deep corner was headed into the side-netting by Songo'o at the far post.
As the half-hour mark ticked by, both sides threatened from corners. Songo'o again steered a Pedersen delivery just wide, whilst Joe Clarke headed Leon Clowes' corner over at the other end.
After a lull in the proceedings, the game sprung to life just before the break.
On 41 minutes, a Rovers corner came out to Bradley Orr, who crossed for Hanley, but his header hit compatriot Rhodes on its way to goal. On the follow-up, Fernandez lifted the ball over the top to Songo'o, who had time to pick his spot, but his thunderous strike was superbly saved by Coughlin at point-blank range.
Straight up the other end, Thornton played in Ormerod, who blazed over the bar.
A minute later, Judge wriggled his way through, one-on-one with Coughlin, but again the keeper made a smart save and Rhodes rattled the woodwork on the rebound.
The final chance fell to Wrexham on the stroke of half-time, as Johnny Hunt's dipping volley forced a fine fingertip save from Kean.
Both sides rang the changes at the break, with an entirely new Rovers XI taking to the pitch, including summer signings Taylor, Simon Eastwood and Todd Kane.
Rovers almost equalised nine minutes after the restart when Diogo Rosado found John O'Sullivan, who cut inside onto his left foot, before firing a crisp strike from outside the box that beat Coughlin, but bounced back off the inside of the post.
Nine minutes later and Rovers created another opening. Josh Morris crossed from the left, Bruno Ribeiro headed down when he seemed certain to go for goal and Taylor fired over the bar.
On 70 minutes, Kane got to the byline, before pulling the ball back to Anton Forrester, whose goal-bound shot was deflected wide.
Moments later, Jack O'Connell replaced Antony O'Connor for his senior bow.
Once again, a subdued half came to life at the death. Two minutes into added time, Forrester robbed replacement keeper Louis Gray of possession, before laying the ball back to Dunn, whose left-foot shot was cleared off the line.
A minute later and the travelling Rovers faithful were celebrating a deserved equaliser after a sustained spell of pressure. Dunn lofted the ball into the box and Taylor rose to head home.
The Rovers players now head off to Portugal, where they will meet Portimonense next weekend.
WREXHAM FIRST HALF: Coughlin, Tomassen, Stephens, Clowes, Creighton, Clarke, Hunt, Evans, Reid, Ormerod, Thornton.
WREXHAM SECOND HALF: Coughlin (Gray 77), Parle, Wright, Collins, Ashton, N'Tame, Royle, Hunt (Cartwright 71), Rushton, Morrell, Reid (Smith 64).
ROVERS FIRST HALF: Kean, Orr, Songo'o, Hanley, M. Olsson, Fernandez, Judge, Pedersen, Nunes, Best, Rhodes.
ROVERS SECOND HALF: Eastwood, Kane, O'Connor (O'Connell 73), Givet, Morris, Ribeiro, Dunn, O'Sullivan, Taylor, Rosado, Forrester.