But Gomez showed nerved of steel once more to score what turned out to be the winning goal from the spot early in the second half, after Jermain Defoe had been brought down by James Ward-Prowse - an incident that also saw the Southampton man dismissed for a professional foul.
"That (his nerve) is the reason Gomez is the first-choice penalty-taker," said Advocaat.
"He did well with the pressure, especially with the second one."
Pantilimon redeemed himself for his part in the Saints' equaliser with a brilliant save from Toby Alderweireld in injury-time.
Advocaat grinned: "That's the reason why he is the goalkeeper! He had to save that ball after the first goal."
Advocaat was also quick to praise Graham for his performance, which saw him win the first penalty and also play a part in the build-up to the second,
He said: "Like the other players, he works so hard, and he was dangerous when he got the ball.
"He protected it well, and that's why created chances.
"They weren't great chances, but there were four or five possibilities against a team that is defensively very strong."