Sam Winnall came close for Barnsley in a quiet first half, but his close-range shot was scuffed wide.
Evans, who joined on loan from Manchester City hours earlier, fired a low strike across Nick Townsend in the second half to put Walsall ahead.
Former Barnsley man Milan Lalkovic scored from 15 yards to ensure the win which kept Walsall second in the table.
The Saddlers, who are unbeaten now in seven away league matches, remain two points behind league leaders Gillingham, while Barnsley slipped to 19th in the table.
Walsall manager Dean Smith told BBC WM:
"George Evans looked top notch. He is a really good footballer, someone we've been keeping tabs on for a while.
"We were outstanding in the second half. We played some really good football.
"It's a great away record and the players deserve it because they've been excellent. But, If I'm being really picky it could be six wins because we should have won at Peterborough."
George Evans scored on his Walsall debut to consign Barnsley to their fourth consecutive league defeat.