The Barcelona midfielder scored the opening goal of the game on the hour mark, before Manchester City's Alvaro Negredo added to Spain's tally with 12 minutes remaining.
The world and European champions were made to work for their win by a disciplined Belarus side who were difficult to break down, and they were given a fright when Sergei Kornilenko scored for the visitors in the 88th minute.
Vicente Del Bosque's side will guarantee themselves a place in the World Cup if they draw with or beat Georgia at home on Tuesday, and will only have to go through the play-offs if they manage to lose, and France beat Finland by a large enough margin.
"I'm happy, above all for the team and the three points," Xavi told Telecinco after the game.
"We had to make a real effort, we were sloppy in the final pass and we needed to be more precise, but we've taken a huge step towards qualifying for the World Cup."
The 33-year-old acknowledged that Spain struggled in the face of their opponents' ultra-defensive approach.
"It's tough when they close up shop. They allow you to enter their half and put 10 men behind the ball," he said. "We tried to move the ball around quickly and be fluid, but sometimes we had trouble doing that.
"We had chances but the goal just wouldn't arrive. My goal and then Alvaro's helped relax us, but Belarus' goal at the end gave us a little scare."
Del Bosque said he was not surprised by Belarus' tactics, but explained he was disappointed with his own team's attitude after going 1-0 up.
"The game had the script we expected, all our opponents play the same way," he told Telecinco.
"We weren't able to break them down but the important thing is that we won and we are closer to our objective.
"We wanted to play deeper down the wings, but when we scored we adopted a conservative spirit and it was to our detriment, I think that we should have tried to be more ambitious."
The coach admitted that Swansea striker Michu did not enjoy the best of debuts, but defended the decision to start him over Negredo.
"Watching Michu train encouraged me to pick him, he has great spirit and gets in good places to shoot," he said.
"It was difficult for him but we have a lot of faith in him. Then Negredo came on and scored, which is what we'd hoped for. We pick the team without worrying about players' egos and it was a good day for Michu to play, that's all."
The coach also refused to be drawn on his future with Spain after the World Cup, when his current contract expires.
"I will speak about that when the moment arrives, but now's not the time," he said.
"We are fighting to qualify for the World Cup and we still haven't done it."