Armin Veh's men signalled their intentions with two goals inside five first-half minutes from Takashi Inui and Olivier Occean.
Hamburg pulled a goal back on the stroke of half time through Heiko Westermann, but they also lost Petr Jiracek to a red card before the interval.
Aigner gave Frankfurt a two-goal cushion to sit on in the 52nd minute, but Heung Min Son made a game of it by scoring a second for Hamburg in the 63rd minute, setting up a tense finale in which Frankfurt held on to join Bayern Munich in a share of top spot.
Frankfurt coach Armin Veh said he did not want to dampen the enthusiasm after his side's back-to-back wins on their return to the top flight and Inui added to it with the opening goal in the 13th minute.
A defensive mix-up let the Japanese forward in and he provided a composed finish after entering the penalty area.
Five minutes later, a capacity crowd was on its feet again when Canadian striker Occean pounced on a loose ball inside the penalty area following a corner to make it two.
Van Der Vaart, making his second debut for Hamburg and welcomed like the Messiah in the northern Germany city, could not fathom a way out of the mire either, so coach Thorsten Fink sent Dennis Diekmeier on for Michael Mancienne.
It had the desired effect with Westermann pulling a goal back just before half time when he powered Artjoms Rudnevs' knock down in from Van Der Vaart's corner.
Hamburg's joy was short lived, though, with Jiracek given his marching orders in first-half stoppage time for a crude foul on Anderson.
Frankfurt soon took advantage of the extra man to re-establish a two-goal lead in the 52nd minute with Aigner rounding off an excellent team move involving Alexander Meier and Pirmin Schwegler by lifting the ball over Rene Adler in the Hamburg goal.
Son reduced the arrears just 10 minutes later with Van Der Vaart setting up the South Korean striker to dribble round Kevin Trapp and stroke the ball home.
However, Fink's side were unable to find an equaliser as they remained stuck to the foot of the table with three defeats in as many games.