Brazilian winger Costa played a fine ball to Mario Mandzukic on the left before slotting home a well-timed pass from the Croatian in the 16th minute at the Allianz Stadium on Monday.
In the second half Genoa went on the attack in search of an equaliser, but six-time defending champions Juventus were able to successfully avoid the equaliser in their bid to secure the year's first win.
Then Costa found Stephan Lichtsteiner in the opposing box, and his neat ball across goal was hacked away from the Genoa goalmouth. The ball then fell again to Sami Khedira but the German midfielder's effort was well held by visiting goalkeeper Mattia Perin.
The final 10 minutes saw Genoa attempt to apply more pressure in getting more numbers forward, but they were unable to breach the Bianconeri's defence as Wojciech Szczesny was left untroubled in the Juventus goal.
Following the win, Juventus have 53 points -- 10 ahead of third-placed Lazio.
"Our aim was to get the three points, though - the lads knew that and they all worked hard to that end," Juventus chief coach Massimiliano Allegri was quoted as saying by his club's website.
"The lads are doing well and it was important to win today to stay on Napoli's heels, keep the teams behind us at a distance and start again after the break with a home win," he added.
"Napoli are ahead of us at the moment but we just need to hang in there and wait for the right moment."
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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