Defending champion Alcaraz reaches Rio Open semi-finals
The 19-year-old Spaniard notched his third win in three matches against 32-year-old Lajovic, including a quarterfinal win over the 80th-ranked Serbian in the quarter-finals at the Argentina Open last week.
Alcaraz went on to win that title to cement his return from a four-month injury layoff that saw him miss the Australian Open.
In the semi-finals on Saturday, Alcaraz will face Chilean qualifier Nicolas Jarry, who toppled sixth-seeded Sebastian Baez of Argentina 6-3, 7-6(3).
Alcaraz is seeking to defend the title that made him the youngest-ever winner of an ATP 500 tournament last year.
Second-seeded Briton Cameron Norrie booked his semi-final berth with a 4-6, 6-1, 6-4 victory over Bolivian Hugo Dellien.
Norrie, trying to reach his third final of the year, will face Spain's Bernabe Zapata Miralles, who beat compatriot Albert Ramos Vinolas 6-4, 2-6, 6-4.
Alcaraz improved his perfect record in 2023 to 7-0, but he had to figure some things out along the way.
"It was a very complicated match," Alcaraz said. "Dusan has a great forehand, a great backhand, a great serve, very good shots, and today he has shown it, he has given a recital.
"But I was solid. In the end, I was very happy to have solved those problems."
Alcaraz trailed 2-4 in both sets, reeling off the last four games of the first before finding himself in another battle in the second.
He belted 32 winners to Lajovic's 13 and won 16 of 17 points at the net.
But 25 unforced errors contributed to the difficulties that saw him go down an early break in both sets.
In the second, he broke back with a stinging backhand winner to level the set at 4-4.
He led 40-0 in the 11th game only to surrender his serve and saved a set point on the way to a break in the next game that forced the tiebreaker.
"Those moments are where the very good players differ from the rest of the players, and I try to play at my highest level," Alcaraz said.
Alcaraz, whose five titles last year included the US Open and made him the youngest-ever world number one, was dominant throughout the decider, putting it away on his first match point with a forehand passing winner.
