Joao Cancelo and Joao Felix scored in each half to earn Barcelona a 2-1 comeback win at home against Porto that took the Group H leaders to 12 points from five matches.
A draw against already-eliminated Antwerp in their final group fixture will be enough to seal top spot.
"We needed this after two years," Xavi said. "We reacted well and displayed a winning mentality on several occasions.
"This was an important step in the right direction. It means a lot to the club.
"That's the first of our targets achieved in the Champions League. It has calmed us down and boosted our confidence, especially that of the players."
Tuesday's win comes on the heels of a disappointing 1-1 draw at Rayo Vallecano in LaLiga, a result which saw them slip to fourth, four points behind arch-rivals Real Madrid.
"The feeling is of happiness and of doing things well. We are progressing. But I don't feel liberated, I feel happy," the Spaniard said.
"You never solve all the problems at Barcelona, but it's a day to congratulate the team and the club for advancing.
"There are many things to improve, of course. We have to be humble. We have done some things very well, others not so," said Xavi, adding that he hoped the victory would be a turning point.
Barca next host Atletico Madrid in the league on Sunday.
