Buoyed by winning three of their past four matches, Blackburn raced into the lead after less than six minutes when an accurate cut back from Ryoya Morishita found Japanese compatriot Ohashi to sweep home first time into the roof of the net, leaving City keeper Radek Vitek helpless.
That early goal seemed to spring City into life and a long ball from Cameron Pring was misjudged by Rovers defender Sean McLoughlin and flicked towards goal by Riis but his effort was shovelled around the post by Balazs Toth.
It was an excellent reaction from the Robins but they wasted another presentable opportunity when Twine uncharacteristically hammered an effort from the edge of the box well over the bar under pressure following a short corner.
In a pulsating opening 15 minutes, a curling delivery from Tomi Horvat found Riis in the middle but he was unable to purchase enough power on his header as Toth made another save to keep his side in front.
Moments later, Riis was not to be denied his goal, capitalising on a poor clearance from Hayden Carter by taking one touch to trap on his knee and a second to volley home into the far corner to level the match.
Twine then thought he was upended by Blackburn wing-back Harry Pickering and the City man would have been clean in on goal but referee Matthew Donohue waved away the visitors' protests of a foul.
Slovenian international Horvat then went centimetres away from giving the visitors the lead when his bending left-footer from 25 yards beat Toth but hit the base of the post and rolled to safety as Blackburn continued to live dangerously.
The Robins' excellent attacking display was eventually rewarded with a lead at the break though when Riis turned from scorer to provider on the 30-minute mark, firing in a low ball which was met superbly on the swivel by ex-Burnley man Twine for his ninth Championship goal of the campaign.