Juventus welcomed the Europa League champions looking to stretch their 17-match unbeaten run at home in Europe with a win that would get the tournament co-favourites off the mark.
But despite dominating for long periods yesterday, Higuain's second-half header notably coming off Sergio Rico's crossbar, the Serie A champions were left frustrated by Jorge Sampaoli's visitors.
"I'm disappointed we had to settle for a scoreless draw because everyone was expecting us to win three or four-nil," admitted Juventus coach Massimiliano Allegri.
"We played well throughout and we barely conceded a shot on goal but we have to work hard to improve. We have five other games in which to secure our passage to the next round, but this game is a reminder that in this competition you have to keep your feet on the ground."
Sampaoli, who replaced current Paris Saint-Germain coach Unai Emery over the summer, had promised attacking football from the Spanish league side.
They offered anything but in a game that, ultimately, went in their favour. And former Chile coach Sampaoli admitted they will have to improve if they are to dream of making the last 16.
"We have to still improve in certain areas, in our pressing and attack notably. Every game we have to try and do better," he said.
"But starting with a point in Turin is good for us." After a one-sided encounter, Juventus were rueing a host of possible scoring chances. In the opening minutes Higuain's midfield interception allowed Dybala to send Khedira through on goal, but the German skewed his shot wide of Rico's far post.
When Dybala produced some magic with a superb mid-air lob to set up Khedira again, the central midfielder fired straight at the onrushing Rico.
Sevilla finally fashioned a rare chance but Sergio Sevilla finally fashioned a rare chance but Sergio Escudero's drive following a poor Juve clearance from a free kick was no problem for Gianluigi Buffon, who collected down low.
Despite Bosnian midfielder Miralem Pjanic sitting on the bench after hitting his maiden goal for Juve on his first start last weekend, Allegri resisted the temptation to shake up his midfield at half-time. And initially, he looked to have made the right decision as Juve enjoyed another flurry of chances.
Mario Lemina's intelligent ball for Evra saw the France defender bundle past Pablo Sarabia on the left to deliver for Higuain, but the cross came up short.
A deft touch from Dybala with the outside of his boot sent Alves free down the right to leave the Sevilla defence desperately chasing back. Higuain rose to meet the ex-Barcelona winger's cross only to fire his header off the crossbar.
Finally, the game looked to be coming to life. Indeed, even Sevilla were entertaining thoughts of scoring a goal. On 66 minutes second-half substitute Joaquin Correa did well to dribble his way past Giorgio Chiellini but his shot across the bows failed to worry Buffon.
At the other end, Rico did brilliantly to get down low and push the ball to safety after Alves's low drive for Dybala a yard from the goalline.
Allegri finally buckled, replacing Asamoah with Pjanic and Evra with fellow wing-back Alex Sandro with 22 minutes remaining.
Juve continued to dominate, but Higuain spurned another chance when he sent Khedira's cross wide of the upright and five minutes later Pjanic dragged his shot wide of the posts.
Higuain, on 80 minutes, fired wide and in the final seconds their frustration continued when Rico pulled off a great save down low to thwart Sandro when the Brazilian sent a diving header towards the near post.