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.
"We've done that over the last couple of seasons."
Whitehead came off the bench to combine with another substitute in Michael Kightly for the winner after Jones' perseverance had forced the error from Olsson.
Pulis said: "I'm really pleased for Deano, because he's been out of the team suspended and he had to wait his time.
"He is one of the bedrocks of the football club is Deano. He has a great attitude and I was so pleased to see him score."
Pulis added: "Winning the first away game is a monkey off our back but we've deserved to win games this season, maybe more so than last season, because we have played well.
"We've drawn four away games and lost at Norwich when we didn't deserve to lose. The games we've drawn, we could have won two or three of them.
"But you need to put the ball in the net and luckily Deano has come on at Albion and done that for us."
Pulis was particularly pleased with the win as, in addition to Crouch, Stoke were also without injured strikers Cameron Jerome and Michael Owen.
He said: "We lost Cameron in the warm-up with an ankle problem and Michael was out as well.
"We weren't going to play Michael but we wanted him to come along and watch the game and he felt his hamstring tighten up again. We think it's because of the cold weather more than anything.
"We couldn't put Michael on the bench so we were three forwards short and still managed to get a result which was fantastic."
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