Daryl Janmaat opened the scoring for the Hornets at Selhurst Park after just three minutes, but the Eagles drew level through Bakary Sako on 89 minutes before dramatically snatching all three points thanks to James McArthur's strike in the second minute of injury time.
The victory for Palace extended their unbeaten run to six games and saw them climb above West Bromwich Albion into 17th place in the table, which left Hodgson delighted and determined to keep climbing away from danger.
"We got a late winner against Stoke as well and had disappointment on Saturday (in the 2-2 draw with Bournemouth), so we've gone through the full range of emotions," Hodgson told BBC Sport. "We've done well in the late stages of games, so I've got to commend the players' attitude and determination to keep going even when things don't look like they're going our way.
"It is a huge three points. Where we are in the table every three points is unbelievably worked for. The moment we think our problems are over is the moment our problems will begin. We have a mountain to climb and it's wonderful to win but we're still very close to the bottom of the table because we haven't quite made up from getting zero points from the first seven games.
Palace could yet slip back into the relegation zone on Wednesday night as current bottom three sides West Brom, West Ham United and Swansea City are all in action.