The goals brought Suarez's tally up to 21 league strikes this season, making him the division's top scorer ahead of Robin van Persie.
Downing, who opened the scoring for Liverpool, believes that the Uruguayan must be a nightmare for defenders to face due to the constant threat that he poses.
"He must be a nightmare for defenders," Downing told ESPN.
"He can be quiet in games and you've got to be on your toes at all times because he can score anything out of nothing.
"You saw that with his goals today, top quality finishes. He's been brilliant for us all season."
The win lifts Liverpool up to seventh in the Premier League table.