The Belgian side took the lead after 31 minutes through Dieumerci Mbokani but Mladen Petric equalised from the spot for HSV three minutes before the interval and Ruud van Nistelrooy completed the turnaround on the stroke of half-time.
The return leg will be played next Thursday in Belgium with the winner set to take on either Fulham or Wolfsburg in the last four.
The final will be played on May 12 at Hamburg's HSH Nordbank Arena.
The game started with a questionable decision in the first minute as Victor Ramos appeared to yank down Van Nistelrooy in the area but referee Martin Atkinson did not blow the whistle.
The visitors grabbed the lead in the 31st minute from a set-piece, Mbokani heading home Sebastien Pocognoli's corner from eight yards.
Hamburg responded well, Van Nistelrooy blasting a fierce attempt off the right-hand post after 36 minutes and shooting wide from 11 yards three minutes later.
The hosts finally equalised three minutes before the break from the spot.
Marcos Camozzato brought down Jonathan Pitroipa in the area and Petric stepped up to blast the ball right down the middle as Standard goalkeeper Sinan Bolat dived to his right.
There was still time before the interval for Hamburg to go ahead as Dennis Aogo's cross from the left side was met by Van Nistelrooy, whose first-time left-footed effort found its way under Bolat and in at the far post.
The first chance of the second half fell to Petric, but his left-footed attempt sailed just wide of the far post in the 64th minute.
Standard went within a whisker of levelling a minute later when Igor de Camargo looped a ball over the Hamburg back-line to Mbokani. His initial header hit the bar and his rebound attempt flew just wide.
Piotr Trochowski was close to doubling Hamburg's lead with 14 minutes left only to see his free-kick from 17 yards fly narrowly over the crossbar.
Bolat then made a fine save from Guy Demel's header with four minutes left to give Standard hope heading into next week's second leg.