Jones made his first Premier League start of the season after Peter Crouch was ruled out after having two teeth knocked out during the midweek success over Newcastle.
The Trinidad and Tobago international was a constant threat and forced the mistake out of Albion defender Jonas Olsson which led to substitute Dean Whitehead netting the 75th minute winner.
Shawcross said: "Kenny was superb. At times he was playing by himself up front and running onto his own flick-ons.
"It was a great performance from him and it justified playing him but he's been fantastic even though he's not been in the starting line-up.
"When he comes on he's very different. I think he showed all his qualities and how big an asset he is to us."
Stoke have now taken 13 points from their last five games and recorded their first away league win in 11 months at the expense of Steve Clarke's side.
But the triumph against the Baggies should not have come as a surprise given their record against them.
Stoke are unbeaten at The Hawthorns since 2003 and lost only two of 30 meetings between the clubs stretching back to 1989.
Shawcross said: "To come to a team that have done so well this season and win is a fantastic three points.
"To get the first away win is massive but over the last couple of years we've done well at Albion.
"It's a great record. Ever since I joined the club we always seem to do well against them.
"We've been on a very good run and now we'll be looking to continue it next week at Aston Villa."
But Shawcross is adamant Stoke will not be carried away with their expectations for the campaign after climbing to ninth position.
He said: "As every other year, we try and reach the target the gaffer (Tony Pulis) sets out for us.
"We then try and push on from that. We want to hit the 40 point mark and kick on from there."