The result extended Alcaraz's winning run at the grass-court Grand Slam to nine matches but the Spaniard could face a tricky test in his next match against American 29th seed Frances Tiafoe who beat Borna Coric 7-6(5), 6-1, 6-3.
Third seed Alcaraz broke for a 4-2 lead as Vukic miscued an overhead smash at the net but the Spaniard handed the advantage back to his 69th-ranked opponent three games later and was broken yet again in the opening set to trail 5-6.
He recovered to force a tiebreak, where he took a healthy 5-1 lead, but allowed Vukic to win three straight points only to raise his level again and take the set as Spanish fans breathed a sigh of relief on Court One.
From there, it was a ruthless performance from Alcaraz as the Spaniard showcased his explosive power and delicate touch as he racked up 40 winners to blow Vukic away.
"I'm really happy about my performance. The first set was the key for me. He served for the set, then I played a really good tiebreak. In the second set and third set, I played at a really high level. I'm really happy about it," Alcaraz said.
"It was difficult for me to close the (first) set. I knew it was going to be the same. I had to be there. I put a few returns in, a few winners. It was a good game for me on the return side.
"In those situations, you have to increase your level, put the early ball in, try to be aggressive with your style. That's all I thought about in that situation and it was helpful."
The French Open champion, who is bidding for a fourth Grand Slam title, did not give Vukic any more opportunities and closed out the second set quickly before easing through the third.
Alcaraz said he was relishing his clash with Tiafoe, having beaten the American en route to his U.S. Open triumph in 2022.
"I'm going for him. We played a good match in the U.S. Open (semi-finals). I know he's a talented player, a tough one, even tougher on grass with his style," Alcaraz said.
"Good volley, good slices. It's going to be a difficult match. I'm ready to take that challenge, put on a show."
