The Earthquakes snatched a freak third-minute lead at Buck Shaw Stadium when keeper David Bingham marked his professional debut by scoring from 90-yards, with a vicious bounce deceiving luckless opposite number Boaz Myhill.
The Baggies, playing their first match since their 3-3 draw at Newcastle 51 days earlier, squandered several chances before going further behind on the stroke of half-time through Khari Stephenson's 30-yard drive.
Thomas pulled a goal back eight minutes after the break with an equally impressive effort, skipping past two Earthquakes defenders before firing into the top corner from the edge of the box.
Several more opportunities came and went for Albion - and it wasn't to be.
New boys Billy Jones and Gareth McAuley made their debuts as second-half subs while Pablo Ibanez and Marek Cech were the only members of the 19-man squad that flew up to Santa Clara from the team's Ojai hotel who played the full 90 minutes.
Assistant head coach Michael Appleton branded the game a "good work-out" and said there were plenty of encouraging signs to take into the remainder of the team's 12-day tour of the United States.
"If truth be told, we played well," he told the club's official website.
"We could've and should've won the game comfortably.
"We limited them to maybe three or four chances and we probably had about 10!
"Both their keepers had inspiring evenings. They seemed to get in the way of everything we put in their way."
Appleton was pleased with the way Albion bounced back from their bizarre early set-back.
And he had plenty of sympathy for Myhill, who was staring directly into a setting sun without the benefit of a cap.
"It was a freak goal," added Appleton.
"The ball seemed really light and it took a wicked bounce on what was a hard pitch and looped over Boaz.
"But after the first 10 or 15 minutes, we dominated the rest of the half and had some good opportunities.
"Their keeper kept out both Roman Bednar and Peter Odemwingie a couple of times and he also denied Jerome.
"Their second goal was a screamer after we lost possession about ten yards outside our box.
"Both sides made a lot of changes in the second half but we started quite brightly and Jerome scored a great goal.
"We had plenty more chances but, again, their sub keeper got in the way of everything.
"Boaz had to make one decent save from a free-kick but that was about it."