Justin Rose — who needs a top two finish on Sunday to return to the top of the rankings — shot a disappointing opening 74 at Walton Heath and drops down to one shot off the bottom of the table.
The World No. 2 — who cancelled his pre-tournament press conference citing a stomach bug — refused to blame illness for his poor form but leaves himself some work to do on Friday if he is to make the halfway cut.
Compatriot Tommy Fleetwood outplayed Ryder Cup partner Francesco Molinari, though his own round was not without incident. On the seventeenth, a wild tee shot finished in a cup holder in a buggy which had been parked to the left of the green.
Wallace had set the clubhouse target earlier in the day as he seeks a fifth win in his 50th European Tour start and fourth victory of a season which saw him narrowly miss out on a Ryder Cup wild card.