Reading have a surprise two-goal lead after 45 minutes at the Liberty Stadium thanks to strikes from Pavel Pogrebnyak and Noel Hunt.
The hosts had the first meaningful chance on the quarter-hour mark when Danny Graham met Wayne Routledge's centre with a powerful header but Royals keeper Alex McCarthy was equal to it.
Routledge himself then had the chance to put the Swans ahead but he fired straight at McCarthy.
Reading then went ahead against the run of play through Pogrebnyak, who ran at the Swansea defence on the inside-left before drilling under Michel Vorm.
The lead was doubled moments before the interval when Hunt volleyed in after a shot had deflected up off Angel Rangel.
