The only goal of the game came from Mohamed Salah's second-half penalty.
A sixth win from six keeps Liverpool top of the league phase standings on 18 points, five ahead of second-placed quartet Inter Milan, Leverkusen, Aston Villa and Brest on 13, while Girona remain on three points in 30th place.
Girona suffered their fifth defeat of the competition, but made Liverpool work for the victory and in the opening half had chances to take the lead but were foiled by the visitors' keeper Alisson.
Liverpool struggled against a side happy to sit back and bide their time, but found the breakthrough from the penalty spot with Salah converting in the 63rd minute after Luis Diaz was fouled.
"Six wins out of six, you can't ask for much better than that. It's not easy to do or there would be more teams doing it," Liverpool defender Andy Robertson said.
"We've played a lot better than tonight, we weren't at our highest level, but at this point it's about winning the games and securing qualification."
Girona were pinned back in the opening minutes by Liverpool's pressure, with the visitors creating two early chances.
Defender Joe Gomez was denied his first goal for Liverpool by a reaction save from Paulo Gazzaniga from a close-range header, with the keeper also saving a shot from Darwin Nunez minutes later.
Girona, with every player behind the ball, were happy to break on the counter-attack and Liverpool keeper Alisson, making his first appearance since early October after a hamstring injury, was soon called into action.
Daley Blind completely missed a cross on the edge of the six-yard box but the ball fell to Alejandro Frances and Alisson held his effort at the second attempt, and later punched away a shot from Miguel Gutierrez.
"We competed toe to toe, we had our chances and, well, we have to accept that we lost," Girona's Frances said.
"It's time to move on. The main thing was to have chances against a great team and we had them."
Nunez had another effort saved when put through by Salah and Girona responded with a shot from outside the area by Yaser Asprilla which Alisson parried away for a corner, with Girona growing in confidence.
Alisson was again involved in the opening seconds of the second half, saving from Arnaut Danjuma and Liverpool struggled to break down a stubborn Girona defence before a Donny van de Beek foul on Diaz gave Salah his chance from the spot.
Salah missed a penalty in Liverpool's last Champions League game against Real Madrid, but made no mistake this time sending the keeper the wrong way and the ball into the bottom corner.
Girona never really looked like finding an equaliser with Liverpool maintaining possession much better than in the opening half and leaving the Estadi Montilivi with all three points.
Villa substitutes make impact
Aston Villa substitutes Jhon Duran and Ross Barkley bagged second-half goals to salvage a 3-2 victory over RB Leipzig this morning, in a match marked by a stunning error from keeper Emi Martinez that gifted Leipzig a goal.
With 13 points after six games, Unai Emery's men are just a win away from booking their berth in the Champions League last 16.
John McGinn put Villa on the scoresheet inside three minutes, when he fired in Ollie Watkins' header past Peter Gulacsi. But Lois Openda levelled against the run of play in the 27th minute, when Martinez ventured well out of his net, but misjudged the bounce of the ball, allowing Openda to nudge it past him and score.
Duran put the visitors up in the 52nd minute when he latched on to a pass from Youri Tielemans before unleashing a blistering shot from nearly 30m out.
The home side levelled 10 minutes later when Openda floated the ball to the back post for Christoph Baumgartner to steer in with a volley. But, two minutes after he entered the game, Barkley bagged the winner in the 85th when his long shot took a big deflection off defender Lukas Klostermann and went in.
Leversken topple Inter
In other matches Leverkusen beat Inter 1-0, drawing level with them on 13 points on the table. Brest also climbed to 13 points with a 1-0 win over PSV.
Real Madrid beat Atalanta 3-2, Bayern Munich beat Shaktar Donetsk 5-1, PSG beat RB Salzburg 3-0 and Celtic had a goalless draw against Dinamo Zagreb.
