With Bosnia-Herzegovina being held by Turkey earlier in the evening, Spain knew a victory over Estonia would be enough to guarantee themselves top spot in Group 5. And the European champions made no mistake as they continued their 100 per cent record in qualifying with an eighth win in eight games.
Unlike Saturday's impressive trouncing of Belgium, it was more of a workmanlike display from Spain tonight and although Fabregas gave the hosts a 33rd-minute lead, Vicente del Bosque's men had to wait until the final ten minutes to wrap up the game thanks to efforts from substitutes Cazorla and Mata.
The final scoreline may have been comfortable enough, but Spain took a while to get going and might easily have found themselves trailing inside the opening 20 minutes as Estonia created some problems for their hosts.
Tarmo Kink had the best chance in the 17th minute but was unable to keep his header down after Konstantin Vassiljev's superb cross from the left had cleared Carlos Marchena and found Estonia's number nine unmarked on the edge of the six-yard box.
Soon after that Sergei Zenjov put another opportunity wide at the near post after Estonia had again done well out wide. Those were a couple of uncomfortable moments for Spain, but the hosts awoke from their slumber and were soon creating chances of their own.
Strike duo David Villa and Fernando Torres both fired over from decent openings, before the latter was denied by Sergei Pareiko after some Xavi magic had put the Liverpool hitman through on goal. Torres then saw another effort deflected behind for a corner before Fabregas broke the deadlock just after the half-hour mark.
Fabregas, who was brought into the starting XI by Del Bosque for tonight's match, did well to steal possession deep in Estonia territory and a quick one-two with David Silva left the Arsenal man with only Pareiko to beat, and he did so with aplomb.
That was no more than Spain deserved after moving up through the gears, and it gave them a 1-0 cushion at the break - the same as against Belgium on Saturday.
However, unlike that match in La Coruna where Spain blitzed the Belgians with two goals in five minutes after the break en route to a 5-0 win, Del Bosque's men had to wait until the 81st minute to put more daylight between themselves and Estonia tonight.
Fabregas was also involved in that goal, scooping a pass into the area where Cazorla bundled his way through the challenge of Estonia captain Raio Piiroja before firing a right-footed shot past Pareiko.
That goal ended Spanish fears of a potentially costly late equaliser by Estonia, and Mata wrapped up the win with his side's third goal in stoppage-time.
Cazorla's deep cross picked out Mata at the far post and the Valencia winger showed good control and skill to create a shooting chance for himself before drilling a low effort past Pareiko to complete the triumph.