Van Persie failed to convert from the penalty spot midway through the second half at St Mary's Stadium, but scored two late goals to complete his hat-trick and complete a 3-2 comeback victory for the Red Devils.
"Robin was great," Vidic told MUTV. "I think he's a great player.
"Even in his first game, he did a good job and this one is amazing with three goals to give us three points, which I think are going to count very much at the end of the season.
"He's a good penalty taker but it could happen to anyone. It was not a great penalty, I have to say, but, in the end, he managed to score two more so we got the win."
Van Persie has scored four goals in three Premier League matches for United this season.