Spain seal World Cup spot
The comfortable victory on a sweltering night at the Estadio Romano in Merida meant Vicente del Bosque's side qualified as group winners with two matches to spare and eight wins out of eight.
"It was a good day and even if we perhaps weren't at our best it was enough to secure qualification," Del Bosque said at a news conference.
The European champions found it difficult to play their usual controlled passing game in the early stages on a cramped pitch at the tiny arena and Estonia created a couple of good scoring chances.
Konstantin Vassiljev skipped past Gerard Pique on the left wing in the 17th minute and sent over a fine cross but Tarmo Kink headed wastefully over the bar before Sergei Zenjov just failed to turn in a centre from Andres Oper.
David Villa fired narrowly over from Xavi's pass in the 24th minute and Fernando Torres did the same a minute later after a swift break.
Fabregas struck in the 33rd minute when he exchanged passes with David Silva on the edge of the penalty area and stroked the ball past Estonia goalkeeper Sergei Pareiko into the far corner.
Substitute Santi Cazorla made it 2-0 when he crashed the ball in from close range in the 82nd minute and Juan Mata came off the bench to round off the scoring in added time with a cool finish from Cazorla's cross-field pass.
Their were wild celebrations at the final whistle and cries of "Espana! Espana!" rang out around the arena.
"We tried to do what we could but Spain were a lot better and that's the reality," Estonia coach Tarmo Ruutli said.
"It will be a different story of course in South Africa. There will be a lot of strong teams wanting to win and the World Cup is always a little bit about luck."
Bosnia's 1-1 draw with visiting Turkey in their Group Five clash on Wednesday had set Spain up for qualification and the win followed Saturday's 5-0 thrashing of Belgium.