A second-half penalty miss aside, Bale put in an outstanding performance down the left flank just three weeks after he almost single-handedly destroyed reigning champions Inter Milan at White Hart Lane.
The 21-year-old ran Bremen full-back Clemens Fritz ragged throughout the victory and rattled the crossbar on two occasions against a below-par German side.
Redknapp, whose side remain top of Group A on goal difference with one game remaining, applauded Aaron Lennon for his performance on the right wing but saved the biggest praise for former Southampton player Bale.
"Aaron is starting to go past people which is want we want him to do but some of the stuff Gareth did was amazing," said the Tottenham boss. "Some of the crosses he put in on the run were amazing.
"It was a bit like when we played Inter with their right-back. We had reports about how good Bremen's right-back was, how he likes to get forward and trouble people but Gareth gave him a torrid time again."
Source: PA
Source: PA