Bingham looked in control as he raced into a two-frame lead but Gilbert kept his cool and fought back to take the following four frames.
However a mistake on the green, that saw him pot the black inadvertently, and then a solid break in the next from Bingham took it to 4-4.
Hamilton lifts German Masters to win first ranking event
Bingham's leading 5-4
Image credit: Eurosport
Some bold potting from Bingham saw him take charge of the frame but he had to have a bit more luck when Gilbert potted the blue and a red at the same time, however once he was back at the table he ensured that he progressed into the next round, where he will face 16-year-old prodigy Yan Bingtao.
The world number 70 was ruthless in his demolition of Michael Holt, winning 5-1 to secure his first ranking quarter-final.
Elsewhere, Hamilton beat Selby 5-2.
The opening four frames between Selby and Hamilton were shared evenly, with each player notching two half-centuries.
Image credit: Imago
Hamilton made a break of 68 (overall score of 109) to take the fifth and then edged a narrow frame to make it 4-2 before defending well to win the match.
Hamilton will now face Barry Hawkins in this evening's quarter-finals, after he saw off Ben Woollaston 5-2 in his second-round match.
Carter takes two-frame lead after first session
Carter to face Hamilton in German Masters final
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