Jon Goddard and Sean Murray had good early chances for the Robins before Murray's deflected shot gave them a deserved lead shortly before half-time.
Lloyd Jones made it two soon after the break as he converted Michael Doughty's flick-on from a corner.
Goddard sealed the win, thumping home Yaser Kasim's pass from eight yards.
The win was only Swindon's fifth in League One this season and first in five games in all competitions, while Charlton lost for the first time in seven and conceded more than two goals for the first time this term.
Sherwood was brought in by Swindon on Thursday to support head coach Luke Williams in a move described by the club's chairman Lee Power as "one of the biggest appointments the club has ever made."
Match ends, Swindon Town 3, Charlton Athletic 0.
Second Half ends, Swindon Town 3, Charlton Athletic 0.
Attempt missed. Anton Rodgers (Swindon Town) right footed shot from outside the box is too high from a direct free kick.
John Goddard (Swindon Town) wins a free kick in the defensive half.
Foul by Patrick Bauer (Charlton Athletic).
Substitution, Swindon Town. Ellis Iandolo replaces Michael Doughty.
Goal!  Swindon Town 3, Charlton Athletic 0. John Goddard (Swindon Town) right footed shot from the centre of the box to the top right corner. Assisted by Yaser Kasim.
Foul by Brandon Ormonde-Ottewill (Swindon Town).
Chris Solly (Charlton Athletic) wins a free kick on the left wing.
Substitution, Charlton Athletic. Adam Chicksen replaces Johnnie Jackson.
Attempt saved. Nathan Delfouneso (Swindon Town) right footed shot from outside the box is saved in the centre of the goal.
Corner,  Charlton Athletic. Conceded by Raphael Rossi Branco.
Johnnie Jackson (Charlton Athletic) is shown the yellow card for a bad foul.
Darnell Furlong (Swindon Town) wins a free kick on the left wing.
Foul by Johnnie Jackson (Charlton Athletic).
Chris Solly (Charlton Athletic) wins a free kick in the attacking half.
Foul by John Goddard (Swindon Town).
Delay in match Yaser Kasim (Swindon Town) because of an injury.
Attempt saved. Sean Murray (Swindon Town) header from the centre of the box is saved in the top centre of the goal.
Attempt blocked. Michael Doughty (Swindon Town) right footed shot from the centre of the box is blocked.
Attempt saved. Yaser Kasim (Swindon Town) left footed shot from the centre of the box is saved in the centre of the goal.
Foul by Nathan Delfouneso (Swindon Town).
Jason Pearce (Charlton Athletic) wins a free kick on the right wing.
Substitution, Swindon Town. Nathan Delfouneso replaces Luke Norris because of an injury.
Substitution, Swindon Town. Anton Rodgers replaces Conor Thomas.
Attempt blocked. Yaser Kasim (Swindon Town) right footed shot from outside the box is blocked.
Yaser Kasim (Swindon Town) wins a free kick in the attacking half.
Foul by Andrew Crofts (Charlton Athletic).
Corner,  Charlton Athletic. Conceded by Luke Norris.
Corner,  Charlton Athletic. Conceded by Brandon Ormonde-Ottewill.
Michael Doughty (Swindon Town) wins a free kick in the defensive half.
Foul by Johnnie Jackson (Charlton Athletic).
Attempt saved. Nicky Ajose (Charlton Athletic) right footed shot from the left side of the box is saved in the bottom left corner.
Attempt missed. Darnell Furlong (Swindon Town) right footed shot from outside the box misses to the left.
Corner,  Swindon Town. Conceded by Chris Solly.
Corner,  Charlton Athletic. Conceded by Lloyd Jones.
Foul by Michael Doughty (Swindon Town).
Jason Pearce (Charlton Athletic) wins a free kick in the defensive half.
Goal!  Swindon Town 2, Charlton Athletic 0. Lloyd Jones (Swindon Town) left footed shot from the left side of the six yard box to the centre of the goal. Assisted by Michael Doughty following a corner.
Corner,  Swindon Town. Conceded by Patrick Bauer.
Tim Sherwood's reign as Swindon Town's director of football began with an impressive victory over mid-table Charlton Athletic.