Dunn and Judge netted either side of a Marc-Antoine Fortune strike as the two sides rounded off their preparations for their respective new league campaigns which begin next weekend.
Blackburn forced Celtic goalkeeper Lukasz Zaluska into his first save as early as the eighth minute through a Brett Emerton header, expertly set up by Dunn, and were ahead just four minutes later.
Richie Towell was a surprise starter in the Celtic midfield, but the youngster's first noteworthy contribution was to foul Nikola Kalinic on the edge of the area and Dunn curled in the resulting free-kick.
Celtic were quick to respond and levelled on 17 minutes when Paddy McCourt's clever pass prompted a smart finish from Fortune who slipped the ball beyond Paul Robinson in the Blackburn goal.
Robinson, who has announced his retirement from international football despite being named in the squad for Wednesday's England friendly with Hungary, was almost beaten again when Milan Misun headed over from point blank range.
Gary Hooper limped off for Celtic to be replaced by Morten Rasmussen and the Danish substitute should have scored with his first touch only to badly miskick when played in on goal by Towell following some deft McCourt skill on the left touchline.
Klasnic was denied by Zaluska a minute after the restart, while at the other end Rasmussen failed to connect with an attempted flick a yard from goal after Daryl Murphy's low driven cross from the left.
In the 53rd minute, Dunn's brilliant attempted chip from long range stranded Zaluska, heavily criticised for his indifferent form during pre-season, only to drift onto the roof of the net.
In the 65th minute, Blackburn restored their advantage when Kalinic exploited some poor defending from Celtic's Andreas Hinkel to play in substitute Judge who netted with a well-placed angled drive.
Celtic did push for a late equaliser and probably would have got it but for Robinson whose fine diving stop to tip a fierce Murphy effort over the bar acted as a timely reminder of the quality now lost to his country.