Darren Pratley grabbed the only goal of the game in the 65th minute to inflict a first defeat in nine games on a visiting Royals side who enjoyed the majority of the chances and deserved a point but were repeatedly denied by keeper Dorus de Vries.
Simon Church also headed over from six yards late on when presented with a great opportunity to level matters, before Scott Sinclair came within inches of an injury-time second for the hosts, leaving Swansea celebrating their first double against the Berkshire side for 33 years.
City's lofty position in the league table will make pleasant new year viewing for Rodgers, who left the Madjeski Stadium in December 2009 after just over six months in charge in which he managed a mere five league wins.
The breakthrough came via a set-piece. Mark Gower floated a well-rehearsed deep free-kick to Angel Rangel who chested the ball down before sending a half-volley goalwards which deflected into the path of Pratley and he fired the ball home.