The Spain international came off the bench to score in the 87th minute, before Borja's own goal completed a nervy 2-0 victory for Tito Vilanova's men.
The three points also mean Barcelona extend their lead at the top, whilst also maintaining their 100% start to the Liga season.
"These three points against a well-organised Granada team are very important. They were very disciplined. It was a very complicated match, but we won the three points and that's what's important," the midfielder told the club's official website.
"Tono [the Granada goalkeeper] was spectacular. He saved nearly everything. The only thing that beat him was a shot from outside the area that went into the top corner.
"I'm very pleased that I scored, and for what the goal means to the team. We won the match, and we have a winning dynamic."
"[In] other seasons, we wouldn't have won this match, but tonight we did. This is what it means to have a winning team."
On the subject of the widening gap between the Blaugrana and Real Madrid, Xavi remained coy, and insisted that he will wait until Jose Mourinho's men feature later on Sunday.
"Let's see what they do on Sunday, but so far our record is perfect: 15 out of 15. It's a good dynamic. Let's see what our advantage looks like tomorrow," he continued.
Vilanova's side travel to Sevilla in round six of La Liga. Kick-off next Saturday is at 22:00CET.