The Reds star put in a true captain's performance, picking the pocket of Greece's defence in the second half before calmly slotting the ball home. Jung-Soo Lee scored the first goal.
Meanwhile, France skipper and United ace Patrice Evra has slammed reports of a rift in the camp as "bull" amid rumours team-mate William Gallas is furious he was overlooked for the captaincy.
Les Bleus failed to win their opening World Cup game for the third successive tournament on Friday night as they could only draw 0-0 with Uruguay at Cape Town's Green Point Stadium.
Evra has been handed the captain's armband for the tournament after Thierry Henry's move to the substitutes' bench. That decision by coach Raymond Domenech sparked talk of disunity in the camp, with the more experienced Gallas apparently unhappy at being overlooked and consequently deciding to boycott the media in protest.
Asked about rumours of discontent, Evra said: "That's bull. That's not true.
"The mood is good. William is a professional and he wants to play at the World Cup.
"Everything is okay. I guarantee the atmosphere is very good. It's not a problem."