Coach Vicente del Bosque gave Negredo his first starting spot in place of Fernando Torres and the Sevilla forward took his chance to impress with two goals in five second-half minutes and assists for David Silva and Juan Mata.
Spain had secured their place in the finals with two matches to spare and were missing key players like Xavi and Cesc Fabregas, while Bosnia were sure of a place in the playoffs thanks to Saturday's 2-0 win over Estonia.
The home side put early pressure on the Spanish goal and Iker Casillas had to be at his acrobatic best to keep out a powerful drive from Sejad Salihovic in the seventh minute.
Striker Vedad Ibisevic rounded the Real Madrid goalkeeper shortly after but skewed his shot wastefully wide and Spain then rocked Bosnia with two goals in two minutes.
Keeper Nemenja Supic came off his line to meet Xabi Alonso's floated free kick on 13 minutes but defender Gerard Pique rose superbly to glance a header into the empty net.
Negredo, making his first start for Spain after he was called up last week to replace the injured David Villa, sent Silva clear a minute later and the Valencia forward placed a precise shot through Supic's legs.
Casillas produced more heroics just before the break on his 99th appearance for Spain with a reflex stop to again deny Salihovic before Negredo made it 3-0 on 50 minutes.
Andres Iniesta won the ball on the right and slipped it through to Silva whose pass found Negredo in the centre of the area and he sent Supic the wrong way with a low shot.
Five minutes later he was in the right place at the far post to steer Albert Riera's cross into the net with his thigh from close range.
Substitute Juan Mata ran on to Negredo's through ball to score Spain's fifth in the 89th minute and Edin Dzeko and Zvjezdan Misimovic pulled late goals back for Bosnia.
"I have fought hard to get here and when you get your chance you have to take it," Negredo, who came up through the Real Madrid youth ranks before moving to Sevilla in the close season, told Spanish radio.
"It would be fantastic to go to South Africa next year but I still have a lot of work to do," he added.
The eight best runners-up across the nine European qualifying groups enter the two-legged playoffs to take place on November 14 and 18.
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