The Liverpool striker – despite doubts over his fitness – nodded home an Edinson Cavani cross in the first half before capitalising on an error from Gerrard to net an 88th minute-winner.
Wayne Rooney's first ever World Cup goal afforded England a glimmer of hope in the second half but the joy was short-lived, with Gerrard cutting a forlorn figure as he trudged off the pitch at full-time.
And Suarez admits he did not like seeing his club-mate so upset, having been comforted by the England captain after Liverpool's 3-3 draw with Crystal Palace at Selhurst Park.
"He's the best player I've played with on the pitch,” Suarez said.
"This is an unlucky moment for him. I don't like it when he hurts like this. I said 'Keep going, forget this game, you're one of the best'."