The veteran midfielder chested the ball down in the 41st minute on Sunday (Monday AEDT), before firing a right-footed shot into the top corner.
"To score a goal like that, you have to keep shooting," Modric said.
"I was by myself, controlled the ball, I struck it well and thank God it went in. It was a nice goal and it's always special to score at home in front of the fans at the Bernabeu."
Modric received a huge ovation from the crowd at the Santiago Bernabeu Stadium.
"I'm very grateful and proud of the affection that Madrid fans show me every day," he said.
Vinicius Junior scored Madrid's second goal after an assist from Kylian Mbappe in the 83rd minute to leave Madrid with the same 54 points as Barcelona, who won 2-0 at Las Palmas the previous day.
Barcelona lead on the head-to-head tiebreaker against Madrid. Atletico Madrid are one point behind the two rivals after Diego Simeone's team won 3-0 at Valencia on Saturday.
Modric made his ninth start in 25 league matches for Madrid in a season in which the 39-year-old has played few minutes off the bench. The former world player of the year scored his fourth goal this season with his neat strike to put Madrid ahead at the Bernabeu.
"Modric is a gift for soccer," Madrid coach Carlo Ancelotti said. "We've had the luck of having a legend with us."
Vinícius scored his first league goal since November from inside the area after a nice through-ball by Mbappe, who on Wednesday scored a hat-trick to lead Madrid to a 3-1 win over Manchester City at the Bernabeu in the Champions League playoffs.
Girona, sitting in 12th place, have lost seven of their past eight games in all competitions, including three in a row in the Spanish league.
In other action, forward Nico Williams scored a goal in each half as Athletic Bilbao trounced last-placed Valladolid 7-1 at home.
Mikel Jauregizar, Maroan Sannadi, Oihan Sancet, Gorka Guruzeta and Inaki Williams, Nico's brother, also scored for Athletic.
Valladolid, who have lost six in a row, played with 10 men from the 66th minute after a red card for Stanko Juric.
The visitors had what would have been the 1-1 equaliser in the first half disallowed for offside.
Meanwhile, Isco scored both of his side's goals, including one from the penalty spot, as visiting Betis scored a 2-1 win over Getafe.
In the late match in San Sebastian, Real Sociedad scored a 3-0 win over visiting Leganes.
Before each match, a banner with the words "respect the referee" and "respect soccer" was displayed as players from both teams posed for photos. The campaign follows several complaints from clubs against refereeing decisions and some threats by fans against the officials.
