Dave Diedhiou scored a late winner as Bideford were knocked out of the FA Carlsberg Trophy with a 1-0 defeat at Hendon.
Bideford failed to make their extra man count after Hendon had Casey Maclaren sent off in the eighth minute for leading with an elbow in a challenge with Kevin Squire.
And Bideford were reduced to 10 men in the 69th minute when Rob Farkins was dismissed for a similar offence.
Despite dominating possession, the visitors were restricted to long-range shots and were rarely able to test Berkley Laurencin in the home goal.
The London club made them pay in the 84th minute when Diedhiou met a right-wing cross, beating Steve Oliver with a downward header to win the second round qualifying tie.