Stead took his tally to nine for the season as the Tractor Boys claimed a hat-trick of away league wins, but leaving Barnsley without a victory this year.
But a second-half fightback from the home side saw Malta international Daniel Bogdanovic pull one back to mark his debut after his clearance arrived just hours before the start..
The Libyan born 28-year-old arrived for an undisclosed fee from Bulgarian side Lokomotiv Sofia on an 18-month deal.
Barnsley though were rocked by a nightmare start as Stead proved deadly in front of goal.
A sweet move opened up the home side as David Norris picked out Kevin Lisbie to tee up Stead, who rifled in an accurate shot from 15 yards after eight minutes.
The home side were still reeling when a loose ball into the box caused a mix-up between keeper Heinz Muller and centre-back Denis Souza.
When the pair collided, Stead was hovering to plunder his second of the game by poking the ball into the unguarded net.
Barnsley responded with a crisp volley from Jon Macken that was held by Richard Wright at the near post and a cross-cum-shot from the new striker Bogdanovic that glanced off the bar.
But Ipswich could have stretched their lead when Stead slipped a neat ball to Lisbie, who rifled a shot that forced a fine save from Muller.
From the resulting corner, Gareth McAuley's towering header clipped the bar as it drifted over and when Tommy Miller hit a goalbound shot Muller saved well.