Ousmane Dembele's 90th-minute strike gave the Blaugrana a 1-0 victory over their relegation-threatened opponents at Camp Nou, cutting the gap to leaders Atletico Madrid to a solitary point.
Real Madrid are up next in El Clasico this weekend, with a thrilling three-way title battle looking set to go to the wire.
If any team looks capable of pulling clear it is Barca, who have won 13 and drawn one in LaLiga in 2021, although they were far from their fluent best for long periods on Monday – something Koeman acknowledged.
"You have to know how to suffer in all the games, we knew how to do it. So yes, we deserved to win," he told reporters.
"It is true that we have not been at the level of the last games , but it is normal that sometimes games like this happen.
"I think we lacked a bit of freshness, it could be because of the international break. So yes, we are now able to win our games and be champions."
That Barca's title destiny is now in their hands owes much to France winger Dembele, who is enjoying his most consistent run of form and fitness since a big-money 2017 switch from Borussia Dortmund in 2017.
"Of course he is an important player, he has shown it today with his game, he has given us the points," Koeman said.
"His form this year is very good. Physically he has improved a lot and that has been the key to his consistency.
"I would like him to stay with us."
After the match, Barcelona announced Philippe Coutinho has undergone a successful meniscus procedure.
The playmaker has not featured in 2021 due to his knee injury.