Vicente del Bosque's holders had to endure a frustrating 60 minutes against Georgi Kondratiev's side, who are bottom of Group I, until Xavi broke the deadlock with a shot from the edge of the area, and Negredo put Spanish minds at ease with a headed goal on 77 minutes.
Sergei Kornilenko pulled a surprise goal back for the visitors in the 89th minute but Spain rode out the final minutes of the game to claim the three points in Mallorca.
The world and European champions moved three points clear of France at the top of the group thanks to the result and now just need a point from their final qualifier, at home to Georgia on Tuesday, to be guaranteed a spot in Brazil next summer.
There were three surprises in Del Bosque's starting line-up. Victor Valdes was picked ahead of captain Iker Casillas in goal, while Swansea forward Michu made his debut for Spain, and Andres Iniesta was left on the bench, with David Silva preferred.
It was the Manchester City midfielder who had Spain's only shot on target in the first half, hitting a powerful effort on goal from the edge of the area 10 minutes before the break, which goalkeeper Aleksandr Gutor was unable to hold onto, but the danger was quickly cleared.
Silva had headed wide of goal earlier on, while Michu had two chances to open his account for his country, miscontrolling the ball when approaching goal with the first opportunity, and then failing to get enough power on a header for the second.
The 27-year-old did not enjoy the best of debuts, and was replaced by Negredo after 56 minutes.
Belarus' plan to sit back and deny their opponents space in the final third worked for the first half, although they created scant chances.
However, they thought they could have had a penalty when Gerard Pique appeared to block a cross into the box with his arm just before the half-time whistle went.
Del Bosque made an attacking substitution at the start of the second half, replacing Arsenal left-back Nacho Monreal with Iniesta.
Despite having an extra man in midfield as the result of the change, the hosts were still unable to penetrate the visitors' back line, and it took some quick thinking from Xavi to finally break the deadlock.
The Barcelona midfielder received the ball on the edge of the box after Pique had sent the ball back out from the byline, and took an early shot at goal, which flew past the unsighted Gutor and into the back of the net.
It was not the prettiest of goals but it gave a huge sense of relief to Del Bosque's side, who were growing frustrated at their inability to break down their opponents.
The goal did not exactly open the floodgates, but the hosts were able to kill the game off with 12 minutes remaining.
Pedro played Sergio Ramos in down the right hand side with a lovely backheel and the Real Madrid defender recalled his days as a full-back by delivering a quality ball to the near post which Negredo dived to meet and head in from close range.
Belarus got an unexpected goal back with just a minute to go. Sergey Krivets saw a huge gap in the defence after winning the ball back from Koke and played in Kornilenko, who shot first time past Valdes into the bottom corner.
Spain did not panic in the three minutes of stoppage time though, retaining the ball comfortably to see out the victory.