Alvaro Dominguez headed in a Juan Arango free-kick in stoppage time to earn a draw after Van der Vaart, a crowd favourite at Hamburg after his first spell between 2005-08, drilled in a stunning shot from the edge of the box midway through the first half but struck his penalty against the post.
Artjom Rudnevs gave Hamburg the lead again on the stroke of half-time after Martin Stranzl, sent off in the 53rd for conceding the penalty, had levelled.
"It would have been a done deal had I scored the penalty," Van der Vaart told reporters. "After that I had the feeling that it could even all go wrong."
Dominguez's late equaliser left Hamburg, who had beaten champions Borussia Dortmund last week for their first win, 14th on four points while Gladbach are 10th on six.
"I am satisfied because we played a very good game but am furious for giving it away," said Hamburg coach Thorsten Fink.
"We set the pace for 90 minutes and conceded two goals from set pieces."
Hannover 96 continued their stunning run to crush Nuremberg 4-1 with two goals from Ivorian forward Didier Ya Konan lifting them up to third on 10 points.
Hannover, who are also competing in the Europa League, are now unbeaten in 21 successive home games.
Bayer Leverkusen notched their first away win of the season, crushing Augsburg 3-1 to prove right team chief Sami Hyypia who said this week that recovery from a bad start was only a matter of time.
Hoffenheim continued their own recovery with their second successive win, beating hosts VfB Stuttgart 3-0 with Takashi Usami snatching an early lead and Joselu and Fabian Johnson also on target. Stuttgart, who have yet to win this season, are in 17th place.
Werder Bremen came from a goal down to beat Freiburg 2-1 with goals from Joseph Akpala and Aaron Hunt and score their first away win in seven months.
Bayern Munich opened up a two-point lead at the top after beating VfL Wolfsburg 3-0 on Tuesday. Borussia Dortmund dropped seven points behind on eight after squandering a two-goal lead to draw 3-3 at Eintracht Frankfurt who are second on 12.
