But the Yorkshire side made heavy weather of seeing off Paul Sturrock's side after the early dismissal of midfielder Simon Walton.
The Tykes peppered Romain Larrieu's goal with shots and headers but only de Silva's header from a Diego Leon cross eight minutes before half-time, found the mark.
De Silva was guilty of squandering several other chances and Barnsley were also denied by the woodwork and Plymouth keeper Larrieu as their efforts on target went into double figures.
In contrast Plymouth hardly troubled Barnsley keeper Heinz Muller who made a comfortable save to deny leading scorer Paul Gallagher who had the visitors' best effort.
Barnsley earned a last-minute penalty when Leon was brought down in the area and Jamaica international Jamal Campbell-Ryce drove home the spot-kick.
Barnsley should have been ahead early on but for poor finishing, the woodwork and a super save from Larrieu.
De Silva squandered the first chance that came the way of the Tykes after ten minutes when he was in space to meet a cross from Diego Leon but he steered his header wide from ten yards.
On the break Plymouth won a free-kick 25 yards out but leading scorer Gallagher, on loan from Blackburn, fired his shot into the Barnsley wall.
But the Devon outfit suffered a setback after 27 minutes when Walton was given a straight red card for swinging a wild kick at de Silva with the ref close by.
From the resulting free-kick, de Silva came within a whisker of earning the home side the lead but his powerful header from Leon's cross smacked against the bar with Larrieu beaten.
The effort was so powerful it flew out of the area where Bobby Hassell was stationed to crash a stinging shot that brought an excellent save from Larrieu who tipped the ball over the top.
De Silva finally made the breakthrough he deserved eight minutes before the break. Leon was the provider with a free-kick that was swung in from the right and this time de Silva powered an accurate header that took a slight deflection on its way past Larrieu.
The home side should have stretched their advantage early in the second half but Jamie Cureton fired his shot straight at the keeper and de Silva missed out on a second goal when his dipping shot was well saved by Larrieu diving to his right.