Kylian MbappĂ© opened the scoring inside six minutes after pouncing on a stray Ron Schallenberg pass, with Dean Huijsen heading in a second from an Arda GĂŒler corner before the break and Carlos EspĂ adding a third early in the second half to wrap up Real Madrid's preseason unbeaten.
The occasion was overshadowed for large parts by the debuts of three summer arrivals, with Ibrahima Konaté starting alongside Huijsen in central defence before Cucurella and Yan Diomande were introduced around the hour mark, alongside the returning Jude Bellingham, who featured for the first time in preseason after only rejoining full training in midweek.
Cucurella's introduction drew a hostile reaction from the Schalke crowd, some of whom have not forgotten his contested handball at the last European Championship, but the Spaniard brushed off the noise to reflect warmly on his first outing in white.
"Very happy, I think it was a great performance from everyone. A great result before we start. The wait felt long, I'm really looking forward to getting the league started," Cucurella told the club's media after the match.
The left-back, who arrived later than his new teammates having played in Spain's World Cup final triumph, credited years of hard work for both his summer of success and his subsequent move to the Bernabéu.
"There's a lot of work behind all this, all the effort put in over these years has paid off," he said of his World Cup title and the transfer that followed.
Asked about settling into the dressing room, Cucurella praised the welcome he had received from his new teammates.
"They're very good people, they've made it very easy for everyone to arrive," he continued, before addressing the support he had received since signing. "I've received a lot of messages. I'll try to give my best. We all want to win titles in this shirt."
Elsewhere in the squad, Thibaut Courtois started in goal, his first appearance since limping off injured at the World Cup during a match against Spain. The Belgian said his recovery had gone smoothly over the summer.
"I feel really good. I did a lot of gym work over the holidays to be in good shape. I came in two days early and the first days with the team involved a heavy workload. I hope to play a lot of matches and go as far as possible."
Courtois was equally satisfied with what he saw from his teammates against Schalke.
"Today was the last test before we start and it was important to do well. Solid at the back, with chances created, good physically. I see everyone in good shape. This is important as we begin," he said, before outlining the message from his head coach. "He asks us for concentration throughout the match, to play well and seriously."
Real Madrid now turn their full attention to Saturday's LaLiga opener against Espanyol at the RCDE Stadium, the first competitive test of José Mourinho's second spell in charge.