The 40-year-old Scottish midfielder, who has played over 1000 matches for club and country in a 22-year career, curled in a fine injury-time effort to complete a stunning fightback, his side having trailed by two goals at half-time.
Danny Haynes and Danny N'Guessan had put Charlton 2-0 up at Deepdale but Nicky Hunt equalised for the hosts on 57 minutes before Alexander, a late substitute, struck in stoppage time.
Formerly a right-back but latterly a cultured midfielder, Alexander has spent around half of his long career at Preston, but his most high-profile spell came for Burnley in the Premier League in the 2009-10 season.
That campaign saw him break a record by becoming the oldest player to make his top-flight debut at 38.
Last weekend he won the Professional Footballers’ Association Merit Award in recognition of his contribution to the game.
Alexander is renowned for his free-kicks and penalties, and is in the top 10 of oldest players to have scored in the Premier League.
1991: Signed professional terms for Scunthorpe United, aged 19, after spending three years at the club on youth terms.
1995: Joined Luton Town for £100,000 after making over 200 appearances for Scunthorpe.
1999: Rejected Burnley to join Preston, where he stayed for eight years, making over 400 appearances and becoming one of the best set-piece takers in the lower divisions.
2007: Finally signed for Burnley in a £200,000 deal, leaving Preston because they would not give him a longer contract on account of his age.
2009: Played in the Championship play-off final as Burnley beat Sheffield United 1-0, sealing promotion to the Premier League. Burnley spent one season in the top flight.
2011: Released by Burnley, re-joined Preston in League One, spending a few matches as caretaker manager after Phil Brown’s sacking.
2012: Wins the Professional Footballers’ Association Merit Award in recognition of his contribution to the game.
2012: Scored the equalising goal in the final minute of his professional career as Preston fought back from two goals down to draw with Charlton.