Patrick Bauer and Nathan Byrne helped Karl Robinson's men complete a perfect smash and grab, cancelling out Zach Clough's free-kick.
A victory which furthers the Addicks' own play-off ambitions was made all the more impressive considering that they were a man short from the 12th minute onwards following Lewis Page's red card.
After Page was sent off for a professional foul on Josh Vela, Clough then made the punishment count double with a brilliant free-kick, his ninth goal of the season.
But Robinson's side refused to lie down, equalising on 23 minutes when Jake Forster-Caskey's free-kick was turned in at the far post by defender Bauer.
The Addicks then grabbed a shock lead in first-half stoppage time when Forster-Caskey led an impressive counter, feeding Byrne to slot the ball under the advancing Ben Alnwick.
Bolton, now without a win in their last five games in all competitions, threw all they had at Charlton after that and struck the woodwork when Andrew Taylor's cross deflected off Chris Solly.
They failed to seriously test goalkeeper Declan Rudd in the second half, however, as they slipped to a second consecutive 2-1 defeat in front of their own fans.
Charlton, unbeaten since Christmas, have now picked up 11 points from their last five matches to climb to 11th, just six points off a play-off place.
Report supplied by the Press Association.

The UN has said media restrictions and violence meant the environment was not conducive to free, credible elections.
Unrest started in April after President Pierre Nkurunziza said he would run for a third term - something protesters say is illegal.
The president says he is entitled to a third term because he was appointed for his first term, not elected.
The presidential election is scheduled for 15 July. East African leaders have called for a further two-week delay.
Africa news highlights: 7 July
The electoral commission spokesman told the BBC turnout for the parliamentary poll had been low in the districts of Bujumbura where there had been protests, but that in some provinces outside the capital it was as high as 98%.
The ruling party - the CNDD FDD - was ahead in every province of the country, Burundi's electoral commission announced.
They won 77 out of 100 elected seats in parliament, AFP news agency says.
The BBC's Maud Jullien says all of the country's private broadcasters have closed in recent months, and many civil society leaders have left the country claiming their lives were under threat.
At least 70 died and 150,000 people have fled the country.
Reporting on a coup and a crisis... using a music-sharing site
10.4m population
50 years - life expectancy for a man
2nd poorest country in the world
85% are Hutu, 14% Tutsi
300,000 died in civil war
Charlton Athletic came from behind with 10 men to deliver a blow to Bolton Wanderers' League One promotion hopes  at the Macron Stadium.
[NEXT_CONCEPT]
The ruling party in Burundi has won the parliamentary election boycotted by the main opposition parties.