Newport dominated much of a scrappy first-round tie but were undone midway through the first half when Russian striker Pavel Pogrebnyak scored with a delightfully flighted chip.
Nick Blackman added a solo effort near the end but Shaun Jeffers pulled one back for Newport with a header before Craig Tanner made it 3-1.
Reading had opened their Championship campaign with a 2-2 draw at Wigan on Saturday but were lacklustre in the opening stages at the Madejski Stadium.
Newport, 14th in League Two last season, dictated the early pace, with Yan Klukowski shooting wide and then Mark Byrne and Aaron O'Connor forcing home goalkeeper Alex McCarthy into decent saves.
Reading weathered the storm and were rewarded when Pogrebnyak put them in front in the 20th minute, cleverly lobbing the ball over Lenny Pidgeley from 20 yards after an incisive Simon Cox pass.
Newport dominated large slices of the second half but barely troubled McCarthy again. A glancing close-range header from O'Connor and a shot from Byrne both drifted wide.
Reading relied on the quick break and Blackman should have done better after a mazy run only the shoot wildly over. He did the same after another penetrative run deserved a more accurate finish.
Newport ended the game strongly but Blackman at last got it right in the 87th minute, cutting in from the right to beat Pidgeley with a low shot.
Jeffers, a Newport substitute, nodded home in the 93rd minute but Tanner, a Reading replacement, restored the two-goal advantage to seal Reading's passage.