Two tries from Hull winger Peter Fox and the unerring boot of Michael Dobson helped Justin Morgan's side claim a deserved 3-12 win over Salford at Craven Park.
Dobson also added a try to finish with 16 points to add weight to Morgan's claims that this could be a good year for the East Yorkshire side.
It took Rovers less than three minutes to open their account for the 2010 season.
Paul Cooke, operating at loose forward, put in a shrewd kick which was chased by Fox and Salford full-back Karl Fitzpatrick, with the latter bundled into touch as he tried to clear.
From the play which followed Dobson made the initial break before handing on to Cooke, who in turn found Fox and the winger made no mistake in the right corner, with Dobson landing the touchline conversion.
Four minutes later another Dobson kick saw Fox pick up, step inside one man and then beat Fitzpatrick to score. Dobson landed a second superb conversion from the touchline.
But Salford settled itself and pulled a try back on 20 minutes when Ashley Gibson sent in Matty Smith under the posts with Stefan Ratchford adding the conversion.
On 26 minutes Fox could have completed his hat-trick but he could not take the final pass and the ball went into touch.
Rovers had the best of the possession during the half, with Salford defending manfully. The visitors were restricted to sporadic breakouts which still put Rovers under some pressure.
Three minutes before the break Rovers went further ahead when Dobson found Jake Webster and the stand-off raced home to score, with Dobson adding his third touchline conversion to see the Robins 18-6 ahead at the break.
After the interval Rovers were back on the front foot and on 46 minutes Liam Watts was hauled down a yard short of the visitors' line.
As the hosts swung play across the field, Fox was sent away but referee Richard Silverwood brought the winger back for a forward pass.
Jason Netherton also went close but was held short by some determined Salford defence.
Ben Cockayne was tackled high as he raced through in the 51st minute and from the play which followed the final pass was wayward and too difficult for Cockayne to take cleanly.
But Rovers went further ahead on 54 minutes when a clearance kick hit a Salford defender and shot into the air where it was collected by Rovers and the move ended with Webster sending in Dobson for an unopposed run to touch down. The halfback then added the conversion.
There was more woe for Shaun McRae's side when Ben Fisher and Dobson combined to send Clint Newton clear in the 61st minute and then Dobson made it six successful kicks out of six with the conversion.
Salford was not short of spirit as it showed in the 64th minute. Rovers were pressing on the visitors' line when Steve Tyrer made a vital interception and found Jodie Broughton who raced some 49 metres to complete a length-of-the-field movement to score.
Stefan Ratchford added the conversion.