Real Madrid manager Carlo Ancelotti described Rodrygo as a "special forward" after the Brazilian scored the winning goal in the 2-1 La Liga victory over previously unbeaten Real Betis on Saturday.
Vinicius Junior struck for the third game running as Madrid took an early lead at the Santiago Bernabeu, but Sergio Canales soon equalised with a goal against his former club.
Rodrygo secured maximum points for Ancelotti's side just past the hour with his first goal of the campaign as the defending champions made it four wins from four.
"He's a special forward because he can play in any position. He's very quick and very intelligent without the ball," Ancelotti said of Rodrygo, now in his fourth season with Real. "The apprenticeship is over and now he's a Real Madrid player in every way."
Madrid moved three points clear of Betis, but Barcelona trimmed the gap to two after beating Sevilla 3-0 in the later game on Saturday.
Next up for the European champions is a trip to Celtic in the Champions League.
"The team's going through a good patch right now, the squad has a lot of confidence," said Ancelotti. "The most important game of the first part of the season is coming up on Tuesday. We're going to be taking on a team that's on a fantastic run and it's going to be very difficult."
Playing at home for the first time this season as renovation work continues on their iconic ground, Madrid had a lucky early escape when Nabil Fekir appeared to be fouled in the area. The incident went unpunished and was not reviewed, but Fekir injured his hamstring and had to be replaced by Luiz Henrique.
Madrid promptly inflicted a sucker punch as Vinicius raced onto David Alaba's ball over the top, lobbing Betis goalkeeper Rui Silva for the opening goal.
Betis, who began the season with wins over Elche, Mallorca and Osasuna, hit back when Borja Iglesias laid off a throw-in for Canales to drive through the legs of Thibaut Courtois.
Vinicius should have immediately restored Madrid's lead, blazing over a cross from Rodrygo. Silva then made a miraculous stop to claw out Aurelien Tchouameni's header.
Karim Benzema skewed over and then failed to convert from point-blank range moments after half-time, the Frenchman ultimately denied by a crucial touch from Silva.
The Betis keeper again got his fingers to a powerful effort from Luka Modric, but Rodrygo had the final say when he slid home Fede Valverde's pass on 65 minutes.
Atletico Madrid drew 1-1 at Real Sociedad after Nigeria striker Umar Sadiq scored on his debut for the hosts.
Alvaro Morata swept in at a corner in the fifth minute, but Sadiq headed home a second-half equaliser following his arrival from Almeria.
The 25-year-old joined Sociedad on transfer deadline day as a replacement for Sweden forward Alexander Isak, signed by Newcastle last week for a reported £58 million ($68m).
Mallorca and Girona drew 1-1 in the early game.