The first leg in Valencia ended 1-1 with Bremen taking a slight away goal advantage into the Weserstadion clash but things didn't start well for the home side when Villa struck in just the 2nd minute.
When Juan Manuel Mata made it 2-0 on the night just 13 minutes later, it seemed as though Bremen's hopes were dashed but they fought back through Hugo Almeida in the 26th minute.
Their hopes, however, were short-lived when Villa grabbed his second on the stroke of half-time to make it 3-1 in the second leg and 4-1 overall.
But once again, Bremen managed to scrap their way back into the contest Torsten Frings converted a spot-kick 12 minutes after the re-start and when Marko Marin scored five minutes later, it was seriously game on. The score was now 3-3 on the night and 4-4 overall but Valencia held a distinct away goal advantage.
When Villa completed his hat-trick in the 65th minute it finally seemed like they had killed of Bremen but again they came back and made it 4-4 in the second leg through Claudio Pizarro five minutes from time.
Another goal was needed by the Germans to get through to the final eight but the Spaniards held on and booked their spot in the quarter-finals after a thrilling encounter.