Obafemi Martins had headed the visitors in front just minutes after the break, but Bentley conducted the comeback with two delightful strikes from distance, before Tugay added the gloss in time added on.
A lacklustre first half, which Rovers certainly had the better of, ended with neither goalkeeper making a single save.
On 14 minutes, James Milner fired a free-kick into the Rovers wall and Habib Beye blasted just over the bar with the follow-up.
But just a minute later and the home side should have taken the lead. Tugay's threaded pass to Benni McCarthy was flicked through to Roque Santa Cruz, who lifted the ball over the advancing keeper, but wide of the left-hand post.
On 25 minutes, Brett Emerton advanced fully 60 yards unchallenged, before blazing just over and on the stroke of half-time, Shay Given's clearance from outside the box was poor, Bentley robbed David Rozehnal of the ball, but his 40-yard strike towards the open goal drifted just wide of the far post.
But just as they did against Aston Villa in midweek, Rovers conceded the opening goal from a set-piece against the run of play.
On 47 minutes, Emerton gave away a foul on the left touchline, Geremi swung in the free-kick and the unmarked Martins glanced a free header in the bottom corner of the net.
But the visitors' lead lasted just seven minutes. Charles N'Zogbia fouled Santa Cruz just outside the box and Bentley curled a sublime free-kick into the top right-hand corner of Given's goal.
Newcastle almost replied immediately, but Brad Friedel twice denied Joey Barton from point-blank range.
With the scores back level, manager Mark Hughes sensed victory and made a trio of attacking substitutions, which paid an almost immediate reward. On 67 minutes, Jason Roberts and Santa Cruz combined well, the ball dropped kindly to Bentley and the England international drilled home his second of the game off the inside of the post.
As Rovers went in search of a third, Emerton struck the same post from the edge of the area, Santa Cruz's follow-up appeared to strike a defender's arm, Steven Reid's shot then looped up to Roberts, who failed to connect under pressure from Given.
Newcastle piled on the pressure, but it was the home side who looked the more likely of adding to their tally. Roberts cut inside two players before stinging the gloves of Given, whilst Morten Gamst Pedersen placed a diving header just the wrong side of the post.
And in the third minute of time added on, substitutes Pedersen and Roberts broke quickly up field and Tugay was left with the simple task of curling the ball in the back of the net with the outside of his right foot.