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Lukas Jutkiewicz headed Birmingham into an early lead and, although Reading equalised through Yakou Meite, Dean's second-half effort earned them a crucial three points.
Meanwhile, Norwich is powering towards the Premier League after the Championship leader eased to a 2-0 win at Nottingham Forest on Thursday (AEDT).
Teemu Pukki bagged his 23rd league goal of the season and Kieran Dowell doubled their lead before half-time.
Daniel Farke's side look odds on to return to the top-fight after last season's relegation.
The Canaries' ninth successive league win extended their lead over second-placed Watford to 10 points with 10 games remaining.
Barnsley maintained its play-off charge with a 3-1 win at Wycombe, despite the second-half dismissal of skipper Alex Mowatt.
Barnsley striker Cauley Woodrow scored a first half penalty following Ryan Tafazolli's challenge on Michal Helik.
Daryl Dike headed Barnsley's second and, after Mowatt had been shown a straight red card for his challenge on Scott Kashket, the on-loan American added his second.
Uche Ikpeazu scored bottom of the table Wycombe's late goal as they slide towards relegation.