Nabil Fekir, Alexandre Lacazette and Clinton N'Jie were all on target as Lyon moved top of the table provisionally via a 3-1 win against 10-man Guingamp at Stade du Roudourou.
Lyon sit two points clear at the summit, with defending champions Paris Saint-Germain scheduled to play Marseille on Sunday and Aulas believes the French giants are capable of winning their first league title since 2007-08.
"It was a great victory. We made an excellent start. It was a strange week to prepare for this game. Tonight we showed a great team spirit," Aulas told Lyon's official website.
"This was the first step towards a fantastic story. It would be an amazing achievement to win the championship. We are calm and are not getting carried away. We know what we are capable of.
"I truly believe that a lot of things are still going to happen before the end of the season."
Fekir opened the scoring in the 26th minute in fortuitous circumstances, as his 25-yard effort was spilled into the net by Guingamp goalkeeper Jonas Lossl before Lyon top scorer Lacazette doubled the lead with a 39th-minute penalty.
Christophe Kerbrat saw red approaching half-time for a rash challenge and N'Jie sealed the points in the 61st minute, before Claudio Beauvue pulled a goal back with 10 minutes remaining.
"It was important to win to stay in the race," said Lyon coach Hubert Fournier.
"It was a game that we have pretty well mastered. We showed relative intelligence to manage the game."
