The youngster, aged only 17 years and 317 days, is six months older than Anfield legend Michael Owen was when he scored his first league goal for the famous club.
Sterling was inspired by a Rodgers pep talk halfway through the first half, during a break in play when Reading’s Jem Karacan was receiving treatment.
Sterling then took just five minutes to put those words into action, running clear at Alex McCarthy in the Reading goal and slotting home into the bottom corner, after a sublime pass from Luis Suarez with the outside of his boot.
Rodgers was thrilled that Sterling has given him a goalscoring option, especially with Fabio Borini out until January.
“I am pleased for him,” said Rodgers. “It is a part of his game we have been working on. He has got good pace, so once he is on the inside he can break the line and get in behind.”
But Suarez missed countless chances to extend Liverpool’s lead, even if Reading scarcely threatened Brad Jones in the home goal.
As promised, Reading’s Jason Roberts, who came on as a second half substitute, refused to wear the “Kick It Out” anti-racism campaign T-shirt during the warm up.
Reading boss Brian McDermott said: “Jason had his view and it is a very strong view and I respect (it).”