Tom Voyce claimed both Wasps tries, the wing capitalising on good breaks from Jeremy Staunton and Stuart Abbott, their opponents from Llanelli had an early lead with Barry Davies's try, but were kept scoreless in the second half.
An indication that this would be a full-bloodied Anglo-Welsh encounter came in the opening minute, although it was an Irishman who bore the brunt. Wasps open-side O'Connor took the ball into contact head-down and was on the end of a huge tackle from Scarlets number eight Alix Popham.
On came the stretcher, off went O'Connor in a neck brace, and on came replacement Dan Leo to fill the gap in the Wasps back-row. The players took a little while to get going after that, which could explain why Wasps' much-vaunted defence parted to allow Scarlets the game's opening try.
Full-back Barry Davies nipped between two defenders, beautifully stood up opposite number Mark van Gisbergen and raced over the line for a try converted by Mike Hercus. However, the USA fly-half let Wasps off the hook with two missed penalty attempts soon after.
Gradually the English side worked their way back into the game and should have scored with 20 minutes gone as they drove into the Scarlets 22. But prop Ali McKenzie's pass missed all three of his overlapping team-mates with the try-line beckoning.
Van Gisbergen got Wasps on the scoresheet with a penalty, but Hercus got his wonky radar fixed and restored the Welshmen's seven-point lead with his own kick. Another worrying injury disrupted the game and again it was a back-row to suffer, this time Scarlets and Ireland blindside Easterby being knocked cold in a tackle.
The stretcher and neck-brace were called into action again, although the Scarlets skipper was also given oxygen as a precaution, with Dafydd Jones replacing him. O'Connor was taken to hospital for a precautionary scan, while Easterby recovered in time to watch the second half from a touchline seat.
While the 57,212-strong Twickenham crowd showed patience through the stoppages, referee Alan Lewis had run out with skulduggery at the breakdown and Wasps prop McKenzie got 10 minutes in the sin bin for not releasing.
The Londoners survived a scare when Hercus intercepted, only for the Scarlets stand-off to somehow contrive to waste the gilt-edged opportunity. Opposite number Staunton showed how it should be done, though, intercepting Clive Stuart-Smith's pass soon after and sending Voyce under the posts for a seven-pointer.
That saw the second half start with the scores level at 10-10, but with a new referee after Mr Lewis was forced to hand the whistle to assistant Simon McDowell because of a muscle strain. Wasps took the lead for the first time thanks to Abbott's fine break, the centre handing off Dafydd Jones and sending Voyce racing over for his second try, again converted.
With their noses in front Wasps kept the Scarlets pinned back in their own half, helped by a hard drizzle that made any handling treacherous. Two more Van Gisbergen penalties and a drop-goal from replacement fly-half Alex King took the English side a vital two scores clear and the Scarlets at arm's length until the final whistle.
Scarlets: B Davies; M Jones, Watkins, R King, D James; Hercus, Stuart-Smith; John, Rees, J Davies; Afeaki, A Jones; Easterby (capt), G Thomas, Popham
Replacements: Gravelle for Rees (73), Madden for J. Davies (64), Cooper for Afeaki (67), D. Jones for Easterby (27). Not Used: L. Davies, Bowen, G. Evans
Wasps: Van Gisbergen; Sackey, Lewsey, Abbott, Voyce; Staunton, Reddan; McKenzie, Ibanez, Payne; Shaw, Birkett; Worsley, O'Connor, Dallaglio (capt)
Replacements: King for Staunton (54), M. Dawson for Reddan (54), Ward for Ibanez (61), Haskell for Worsley (78), Leo for O'Connor (1), Bracken for Leo (31) Not Used: Erinle Sin Bin: McKenzie (29)
Referee: A Lewis (Ireland)