Chris Brunt rattled the woodwork for the visitors, while Chris Samba came closest for the home side, who had substitute Jason Roberts sent off on his return from injury.
Rovers' biggest following of the season turned out to bid a fond farewell to Tugay, who has made just short of 300 appearances in eight years at Ewood Park.
With Rovers skipper Ryan Nelsen missing with a calf injury, the midfield maestro was handed the captain's armband, while Andre Ooijer, who was also making his final appearance before a summer switch back to PSV, returned to the team in the centre of defence.
The visitors registered the game's first attack with Brunt's early sighter looping off the leg of Gael Givet and over the bar.
But from that moment on, Rovers gained the ascendancy. Samba went close with two left-foot strikes in the space of five minutes - the first whistling just over the bar and the second brushing the outside of the post.
Morten Gamst Pedersen was then denied when his dipping free-kick from 30 yards had to be palmed around the post and from the resulting corner, Tugay fizzed an effort just wide.
As the half drew to a close, Brunt again provided the Baggies' biggest threat.
First he dragged a shot well wide from outside the box, before unleashing a fierce volley from Jonathan Greening's deep cross which required a sensational reaction save from Paul Robinson to tip the ball onto the woodwork.
Both sides had penalty appeals for handball waved away early in the second half, before West Brom started to string together some chances.
Marc-Antoine Fortune headed just wide from Robert Koren's cross, before Brunt and then Juan Carlos Menseguez both failed to hit the target in the space of a minute.
Rovers' task was made doubly difficult when Roberts was shown a straight red card for an alleged elbow on Jonas Olsson just 10 minutes after coming on.
The visitors ought to have won it when the unmarked Greening sent a free header wide of the mark from Brunt's corner and it is due to those missed chances that the Baggies will be playing Championship football next season.