Jordan Rhodes' 13th goal of the season was enough to give Rovers their second away win of the season in a pulsating match at Huish Park.
Both sides played their part in what was a tremendous advert for Championship football.
Rovers ran the first half creating a dozen excellent opportunities but they couldn't find a way past the returning Marek Stech in the Glovers goal.
The second half was a much closer affair as the home side twice struck the woodwork, but it was left to Rhodes to score the only goal of the game on 59 minutes. Firing into the top corner after excellent work from Adam Henley and David Dunn.
Both sides continued to create long into added time, but Rovers saw out the game to make the first competitive match between the two sides a memorable one.
Rovers made just the one change for the trip to Yeovil Town as David Dunn replaced Josh King in the starting eleven. The inclusion of Scott Dann and Grant Hanley meant they both made their 100th appearance for the club.
The match had the atmosphere of a cup tie as Rovers started the game very much on top.
The opening half of the first competitive encounter between the two sides at Huish Park saw Rovers create numerous excellent chances, but took none of them.
Two minutes in and space opened up for Jason Lowe inviting the midfielder to shoot, he tried his luck from the edge of the box but miscued his effort, the ball falling into the path of Rhodes but as he looked to control it ran beyond him.
David Dunn was seeing plenty of action behind Rhodes up front and lovely play by the attacker saw Chris Taylor teed up but the returning Marek Stech saved low down.
Rovers continued to pepper the Glovers area, Tom Cairney with a ball across to Adam Henley, his centre found David Dunn but his header was straight at the Yeovil 'keeper.
Cairney then went for goal himself, but his excellent shot across the area was tipped behind.
Dunn fired wide wide with a volley before another chance fell to the hometown boy, Lowe lofted a ball up to Rhodes and as he nodded down for Dunn he dragged his shot past the target.
For the home side, Joel Grant was lively up front, carrying their threat with his pace. On one occasion it almost saw him through but he scuffed a shot.
That was a rare effort from the Glovers as Rovers continued to create, Dunn saw a shot blocked, Marshall fired over before Cairney was thwarted at the near post.
The first half was summed up with a 36th minute centre from Tom Cairney, a perfect curling ball, all it required was a touch but neither Dunn nor Taylor could connect.
Rovers had some defending to do as the half drew to a close, Tom Cairney cutting out a dangerous centre, before Grant Hanley blocked an Ishmael Miller shot on the turn.
There was still time for one further Rovers chance. On the stroke of half time good play by Dunn saw him feed Jordan Rhodes for his first chance of the half, but Marek Stech saved with his legs.
Rovers were given a scare straight from the restart as a high cross from Liam Davis was spilled by Simon Eastwood in the six-yard box under minimal pressure from Miller, but Rovers were able to snuff out any threat.
Then a low centre from Miller had to be put behind by a sliding Scott Dann. The initial corner came to nothing but as Shane Duffy kept play alive on the far right, he crossed for Lundstram on the left and his first-time shot was acrobatically tipped over by Eastwood.
In contrast to the first half, the second was a much more even affair with both sides creating chance after chance.
David Dunn shot after yet another strong run was kept out by Stech, whilst Eastwood made another good save to deny Miller.
Sensing their chance the home side went the closest as the woodwork was rattled on 57 minutes. A ball into the box dropped to Ishmael Miller but his first-time shot came off the crossbar.
Straight up the other end and Tommy Spurr took on all-comers as he charged goalwards but Stech stood strong to make the save.
The deadlock was finally broken just before the hour mark, and thankfully for the 1074 travelling fans from Lancashire it was they who were celebrating.
Adam Henley started the charge with an advanced forward run, he had the option of Taylor to his right but instead slipped the ball inside to David Dunn. Dunn dropped a shoulder and that gave him space in the area to find Jordan Rhodes who pinged the ball into the top corner of the net leaving Stech with no chance.
After a host of chances had come and gone, the goal was a welcome relief.
But Yeovil came back once again and they rattled the woodwork once more. Jo Ralls with a curling right-footed shot that beat Simon Eastwood but rebounded off the far post to safety.
A host of substitutes followed as both sides made changes. Lee Williamson replaced Chris Taylor, whilst Ruben Rochina replaced David Dunn.
It would be Rochina who would have the next effort at goal and what an audacious one it was. Cutting in from the left it seemed easier to shoot with his right foot but the Spaniard had other ideas, flicking an incredible left-footed shot that Stech did well to tip over.
Credit to the home side they kept coming back for more, the lively Joel Grant fired through the legs of Adam Henley forcing an unsighted Eastwood into making another important stop, before Ed Upson fired wide with a low effort from distance.
However with Yeovil committing bodies up front, there was space to exploit at the back, Ruben Rochina twice going close.
On 90 minutes Rovers held their breath as Miller and Hanley tangled in the penalty area, the home crowd roared for a spot-kick, referee Iain Williamson waved play on as Rovers countered, Stech first denied Cairney and then Rhodes.
Four additional minutes were shown but Rovers played it out the right way, seeing the clock tick down to claim their second win on the road this season.
YEOVIL: Stech, Ayling, McAllister (c), Edwards, Webster (sub Dawson 35 mins), Duffy, Ralls, Davis (sub Hayter 68 mins), Grant, Miller, Lundstram (sub Upson 74 mins).
Subs not used: Stewart (GK), Foley, Moore, Morgan.
Booked: McAllister, Lundstram, Ayling.
ROVERS: Eastwood, Henley, Dann (c), Hanley, Spurr, Taylor (sub Williamson 74 mins), Lowe, Cairney, Marshall, Dunn (sub Rochina 67 mins), Rhodes (sub Gestede 90+3 mins).
Subs not used: Kean (GK), Kane, Kilgallon, Judge.
Goals: Rhodes 59 mins.
Attendance: 7179 (1074 Rovers fans).