Messi struck a dramatic 92nd-minute winner to see Barca edge Madrid 3-2 at the Santiago Bernabeu on Sunday.
The goal was Messi's 500th for the club and came at the perfect moment, reigniting the La Liga title race.
Suarez, who played 90 minutes in the crucial win, hailed his team-mate for his landmark goal.
"The team was great! Everybody's effort was spectacular," he wrote on Twitter, pictured with Messi.
"With the best player in history. Congratulations to my friend!"
The team was great! Everybody's effort was SPECTACULAR— Luis Suarez (@LuisSuarez9) April 23, 2017
With the best player in HISTORY
Congratulations my friend !!!!! pic.twitter.com/0o0oja9PPF
Barca's win moved them top of the table, but Madrid are level on points and have a game in hand.