"This result has been coming for a long while," the Baggies boss said after Saturdays game.
"We've been playing well away but haven't had the breaks. Earnshaw is one of the best players in the country to have as a substitute and it has certainly worked for us today.
"This was a match we needed to win to close the gap at the bottom and with eight matches left we have half a chance of escaping if we keep believing in ourselves.
"I'd have put Earnshaw on even if it had been 11-a-side. It was definitely a late challenge by the Charlton player which got him sent off but in my playing days it would probably have been a booking.
"Hopefully this result will send shockwaves through the bottom of the Premiership table but we still need to win the majority of our remaining matches."