The England Under-21 international, at 17 years and 317 days old, as a result became the club's second-youngest Premier League goalscorer behind Michael Owen.
His strike should not have been the Reds' sole effort but such are their problems up front this season - prior to kick-off only Sunderland (two) and bottom club QPR (one) had scored fewer at home - win-less Reading remained in the game right up until the final whistle.
The first half was virtually one-way traffic but the hosts lacked a cutting edge, too often over-complicating matters with one pass too many in and around the penalty area.
Sterling found himself in the best attacking positions on several occasions but managed to get a shot off on target just once and Alex McCarthy easily held.
Auxiliary left-back Glen Johnson was also enjoying a lot of possession in the final third but he looked more threatening when cutting inside on his right foot.
During an injury break for Jem Karacan, who was eventually forced off by the effect of Steven Gerrard's block tackle, Rodgers took the opportunity to pass on some advice to Sterling.
Whatever he said appeared to have the desired effect as in the 29th minute the England Under-21 international finally made the breakthrough.
Suarez's delicate flick-on was seized by the teenager who raced through the inside-right channel and fired a shot across McCarthy and into the far corner of the net.
There were two main talking points prior to the game and both duly cropped up.
Firstly, Reading substitute Jason Roberts carried out his vow not to wear a Kick It Out T-shirt in the warm-up in protest at his perceived lack of action in combating racism in football.
While the rest of his team-mates - and all their Liverpool opponents except goalkeeper Brad Jones - donned the tops for the pre-match drills the 34-year-old went without, although Garath McCleary and Karacan removed theirs soon after entering the field.
Second hot topic, which has become a regular theme this season, of the week was whether Suarez dives or not.
The Uruguay international had seen one challenge by Kaspars Gorkss go unpunished, from which the striker curled a shot onto the roof of the net, and another given - prompting a sarcastic standing ovation from Anfield before he drilled the free-kick into the wall.
But the third instance, just before half-time, was the most contentious with Suarez going to ground under a challenge from his Latvian marker close to the byline.
Referee Roger East waved play on and then was soon waving away protests from a cluster of Liverpool players as he whistled for the interval.
Suarez, accompanied by the club doctor, gingerly hobbled off well after both teams had left the pitch but returned for the second half, which was less than a minute old when Sterling should have made it 2-0 having turned smartly in the penalty area but fired straight at the goalkeeper.
The South American did not appear to show any ill-effects with only his vision apparently affected as he opted to shoot at McCarthy when he should have squared to the unmarked Nuri Sahin.
Liverpool were almost caught by a swift counter-attack with substitute McCleary forcing an immediate save from Jones, on his first league start for the club in the absence of the injured Jose Reina, who also punched away a Jobi McAnuff shot.
The home side redoubled their efforts as Martin Skrtel flashed a header wide, substitute Jonjo Shelvey, caught in two minds, miscontrolled Suarez's cross and Gerrard saw a narrow-angle shot squeeze through McCarthy's fingers but wide of the post.
Further chances fell to Johnson, Suarez, who missed the target from 10 yards, and Gerrard but needless to say none were created.
Rodgers said he felt his side would "fly" once they secured their first home win.
They will need to as next weekend they make the short trip to near-neighbours Everton, who even after this win are still five points ahead with a match in hand.