Bedford had been this way and lost so many times this season that when they established a seven-point lead through a dropped goal by Sam Howard after 54 minutes, and maintained it when Alex King and Howard soon exchanged penalties, only a brave man would have bet on a home win.
Wasps were having a bad day at the office, which recalled their previous defeat at another basement dweller, West Hartlepool, but Bedford showed their unfamiliarity with being in front when Howard handed Wasps the initiative with too many kicks from hand in the closing stages.
Wasps had too often suffered from too much petulance at close quarters, but Lawrence Dallaglio set a fine example in the vanguard of several rucks as they drove at Bedford and a dreadful pass by the Blues scrum-half, Richard Elliott, at a scrum on Bedford's line led to a pushover try for Dallaglio.
Crucially, King sent the conversion wide of the posts but as the match ticked over into injury time Junior Paramore gave King another chance when he killed a ruck. The Wasps outside half who, remember, was Clive Woodward's first choice for England when the coach took over in the autumn of 1997, was almost head on to the posts from 40 metres out but could not hit the target.
The exchanges continued full pelt, watched from the sidelines by the flankers Jason Forster of Bedford and Wasps' Paul Volley who were serving their time in the sin bin after a dust-up. Paramore joined them for a head-high tackle on Andy Reed, but Bedford held out.
The first half was left looking more than a touch prosaic but that would be to understate the sterling efforts of Paramore who, along with Scott Murray, was offered an extended contract by Bedford in the week.
The Samoan looks the type to run through brick walls at the drop of a hat, never mind for money, and he and Murray did not flinch even when paid close attention by Wasps' hardmen.
It was nip and tuck with two tries for each side, and on-loan full-back Scott Stewart got another for Bedford nine minutes into the second half.
Bedford: S Stewart; R Underwood, A Murdoch (capt), D Harris, D O'Mahony; S Howard, R Elliott; C Boyd, J Richards, V Hartland (A Ozdemir, h-t), D Zaltzman (R Winters, 10), S Murray, J Cockle, J Paramore, J Forster.
Wasps: J Lewsey; P Sampson, F Waters, M Denney (R Henderson, 50), S Roiser (M Friday, 70); A King, M Wood; D Molloy, T Leota, W Green, M Weedon (capt) (S Shaw, 59), A Reed, L Dallaglio, P Scrivener (J Worsley, 57), P Volley.
Referee: N Yates (Cheshire).