Massimiliano Allegri's men were denied extra-time in Madrid on Thursday (AEST) thanks to a controversial late penalty that Cristiano Ronaldo converted to send Los Blancos through 4-3 on aggregate, but it was business as usual in Serie A on Sunday, with the reigning champion comfortably extending its lead.
Gianluigi Buffon was in the spotlight for much of the week following his sending off and outbursts at referee Michael Oliver in reaction to the penalty at the Santiago Bernabeu, though he took something of a backseat for much of the contest as Juve generally controlled things.
Nevertheless, it took Juve until just before the break to craft its first real opening and Mario Mandzukic – who netted twice in Madrid – made no mistake to break the deadlock after a cross from Costa, brought on only a few minutes earlier due to an injury to Miralem Pjanic.
The Brazil international was then vital for Juve's second goal, picking out Benedikt Howedes for his first goal in Italy after an hour.
And Juve wrapped things up 15 minutes from time - Costa completing a hat-trick of assists to set up Sami Khedira, rounding off a straight-forward victory on Allegri's 350th Serie A game as a coach.
Juve wasted little time taking control of proceedings, spending much of the opening stages patiently probing the packed defence of their Europa League-chasing visitors.
But by no means did they regularly craft goal-scoring chances.
Juan Cuadrado was presented with one early on, as Kwadwo Asamoah's deep cross found the Colombian, who struck a wayward volley which was nearly deflected on target by Gianmarco Ferrari.
Sampdoria appeared to take encouragement from its fairly comfortable start and nearly went ahead in the 22nd minute – former Juve striker Fabio Quagliarella forcing Buffon into a crucial save with a header from a tight angle.
The first half looked set to peter out and Juve suffered the blow of losing Pjanic to an innocuous-looking injury.
But his replacement, Costa, made an instant impact, crossing to Mandzukic for an easy finish on the stroke of half-time.
Sampdoria began to see more of the ball after the interval and Duvan Zapata tested Buffon with a header in the 55th minute.
But Juve soon doubled its lead at the end of a well-worked move – Howedes heading in emphatically from another precise Costa delivery.
And Costa was crucial again 15 minutes later, attacking Sampdoria on the right wing and cleverly cutting a pass back to Khedira, who coolly swept home to round things off in Turin.