The teenager capped an impressive first half team performance by giving the hosts a deserved interval lead.
But the Championship side were much improved after the break and Nick Blackman drew them level before substitute Garath McCleary grabbed a late winner.
Paul Cook made eight changes from the side that drew with Morecambe in the league at the weekend.
Matt Clarke, Kyle Bennett and Gareth Evans – now being deployed at right-back – were the only survivors.
Saturday’s last-gasp goal hero Jayden Stockley came in up top, while Paul Jones took his place between the sticks.
There were also starts for Brandon Haunstrup and Adam Webster at the back and Ben Close, Danny Hollands, Adam McGurk and Chaplin in midfield.
It was an open start to proceedings, with both sides looking to get forward without creating any clear-cut chances.
Simon Cox sent a couple of shots off target for the visitors – wearing their distinctive African violet away kit – while Ali Al-Habsi did well to claim a McGurk cross before it could reach Stockley at the far post.
Jones did well to stop the Royals opening the scoring midway through the half when he denied Blackman from point-blank range.
Stockley then should have put Pompey ahead on 27 minutes after Bennett had collected a neat chipped pass from Hollands.
The winger showed great skill on the left and sent in a perfect cross for Stockley, who somehow managed to fire wide from just a few yards out.
Reading then broke quickly up the other end of the pitch and Jones was quickly off his line to deny Hal Robson-Kanu.
The visitors went close again on 37 minutes when Jones palmed away Chris Gunter’s cross and Cox hooked the loose ball over.
Instead it was Pompey who forged ahead moments later – thanks to a fine finish from CHAPLIN.
Al-Habsi beat the teenager to Hollands’ long pass, but made a complete mess of his attempted clearance.
Chaplin was forced out wide, but kept his composure to find the net with a fierce finish from the tightest of angles.
Pompey were not content to sit back on their lead once the second half got back underway.
The hosts made some promising incursions into their opponents’ area, while Al-Habsi did well to beat Webster to a dangerous Bennett cross.
Reading did threaten with a neat passing move just past the hour mark, but it ended with Danny Williams firing harmlessly over.
And the visitors were level on 64 minutes when Blackman cut inside from the right and slotted a neat finish into the bottom corner.
It was the Royals who were now looking the more threatening side and Clarke made a good block to deny Robson-Kanu.
Cook switched things up on 79 minutes, bringing on James Dunne for his first appearance of the season in place of McGurk, with Chaplin making way for Ben Tollitt soon after.
But it was a Reading substitute who made an impact by firing the visitors ahead, as McCleary was left alone to convert at the far post following some good build-up between Robson-Kanu and Stephen Quinn.
Matt Tubbs replaced Bennett for the final few minutes, but the Blues were unable to find a leveller and it was Reading who took their place in the third round draw.
Pompey (4-2-3-1): Jones; Evans, Webster, Clarke, Haunstrup; Close, Hollands (c); McGurk (Dunne 79), Chaplin (Tollitt 83), Bennett (Tubbs 89); Stockley
Goals: Chaplin 40
Subs not used: Murphy, Burgess, Atangana, Roberts
Reading (4-1-4-1): Al-Habsi; Gunter, Hector (c), Ferdinand, Obita; Norwood; Blackman (McShane 89), Williams (Tshibola 90+2), Quinn, Robson-Kanu; Cox (McCleary 69)
Goals: Blackman 64, McCleary 84
Booked: Robson-Kanu, Norwood, Williams
Subs not used: Moore, Stacey, Fernandez, Sa
Referee: Gavin Ward
Attendance: 18,190 (2,082 away fans)