It allowed them to move into sixth and close the gap to Champions League qualification to seven points with nine matches remaining.
"Earlier in the season we would probably have lost the game," Downing told liverpoolfc.com.
"But great credit to the lads, we kept going and the fans were right behind us.
"I'd say it was probably one of the best wins of the season.
"A lot of people have been saying we can't beat teams in the top five or six - that's out of the way now. Hopefully that will kick us on.