Costa, a £32million acquisition from Atletico Madrid in July, scored twice in the opening seven minutes as Jose Mourinho's side geared up for their Barclays Premier League opener at Burnley on Monday with a deserved victory.
The Blues made the perfect start when Costa opened the scoring in the second minute
The Spain striker was unleashed by a fine Ramires through-ball and made no mistake in dispatching past Sociedad goalkeeper Enaut Zubikarai from a tight angle to give the hosts a 1-0 lead.
Costa then doubled Chelsea's lead five minutes later when he tapped home from close range after Andre Schurrle's shot from the edge of the area crashed off a post and into his team-mate's path.
Costa missed a chance to snatch a hat-trick in the second half, while Fernando Torres also fluffed a clear-cut opening.
Thibaut Courtois - largely untroubled for most of the match - had to be alert to deny Chory Castro in the 77th minute.
Source : PA
Source: PA