The Owls were 3-1 winners against The Baggies, who were last season plying their trade against Manchester United and Arsenal - and deserved the win after an outstanding first-half showing.
Glenn Whelan, recalled to the side because Yoann Folly has flu, headed the first and Madjid Bougherra added a second shortly after.
Jason Koumas added a late strike for the visitors but Steve MacLean's last-minute spot kick gave Laws' his first home win.
He said afterwards: "We knew this was always going to be a tough test because West Brom are possible contenders for promotion to the Premiership.
"What epitomised the performance was our hard work and willingness to work for each other and close people down. That was most evident in the first half and that won us the game."
One minus point was the early substitution of left-back John Hills - he could be ruled out of the Leicester City trip this weekend with a hamstring strain.