Earnshaw came on to the pitch in the 64th minute for Kieran Richardson and walked off at the end with the match ball under his arm after taking his goal tally for the season up to 13.
The match turned in the 29th minute when Charlton central defender Talal El Karkouri was sent off for a foul on Albion's Zoltan Gera.
The score was 1-1 at the time and stayed that way until the Welsh international came on to perform his party piece as manager Bryan Robson went for broke and played with three strikers against the tiring ten men.
Earnshaw's goals came at the end of the ground at which the 2,000 delirious Baggies fans were seated after the Midlands club gave them free travel in a 40-coach convoy to London.
An unmarked Geoff Horsfield headed Albion in front after just nine minutes and only a great save by Charlton keeper Dean Kiely denied Gera a second with a fiercely struck free-kick.
But the home side equalised in the 24th minute when Jonatan Johansson raced through the middle of the Albion defence before firing the ball past Russell Hoult as the goalkeeper came racing out of his area.
Then came the sending-off which reduced Charlton to ten men, but they could still have gone ahead before half-time when Hermann Hreidarsson's header was cleared off the line by Darren Moore.
Earnshaw got his first goal in the 72nd minute, scoring from close range after Horsfield had headed Paul Robinson's cross back towards goal.
The little striker then raced through the middle of a non-existent Charlton defence to beat the offside trap and put the Baggies 3-1 in front before completing his hat-trick from the penalty spot after another substitute, Richard Chaplow, had been brought down by Bryan Hughes.
MAN OF THE MATCH: Zoltan Gera (West Brom) – Rob Earnshaw may have stolen the headlines with his quick-fire hat-trick, but it was the Hungarian who laid the foundations for a well-deserved victory with a lung-bursting display in the Albion midfield.