Mikey Moore opened the scoring and Dominic Solanke doubled the lead before the game got away from the Championship visitors.
Substitute Kevin Danso headed in with his first touch after coming on, and debutant Savio marked his introduction with a goal and an assist.
Jones scored a late headed consolation for Charlton, who have made a strong start to the Championship season.
Newcastle came from behind twice to beat West Bromwich Albion 3-2 at St James' Park.
Isaac Price gave the visitors the lead with a free-kick before Bazoumana Touré equalised and Harvey Barnes put Newcastle in front.
Price levelled again from the penalty spot, only for Barnes to restore the lead and settle the tie. It was Matthias Jaissle's first win as Newcastle manager.
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Everton won 4-0 at Preston, with Thierno Barry scoring a hat-trick and Brennan Johnson netting his first goal for the club.
The match marked David Moyes' first return to Deepdale, where he began his managerial career, since leaving Preston in 2002.
The second-tier hosts were unable to trouble their Premier League opponents.
Bradford City produced the upset of the night, knocking out Burnley 4-2 on penalties after a goalless draw.
Burnley, relegated from the Premier League last season, could not find a way past their League One opponents over 90 minutes.
The third-round draw takes place after the fixtures, with nine Premier League clubs in European competition entering: Arsenal, Manchester City, Manchester United, Aston Villa, Liverpool, Bournemouth, Brighton, Sunderland and Crystal Palace.