Luiz Suarez scored a late consolation for Uruguay but the World and European champions dominated the game from start to finish and could easily have won by more.
"We were really tired towards the end of the match. When you are playing in temperatures like this it's normal that should happen," Spain coach Vicente del Bosque said in an interview with Spanish television broadcaster Telecinco.
"We played an excellent first half and I think we also played very well in the second period but we suffered a bit at the end.
"They are three magnificent points which put us in a very good position to get through to the semi-finals."
The FIFA tournament is being used to test Brazil's preparations ahead of the World Cup they host next year and Spain dominated from the outset of their opening match.
Fabregas, Pedro and Andres Iniesta all came close in the first quarter of an hour before a 20th minute corner was knocked out of the Uruguay box as far as Pedro whose fierce shot was deflected by Diego Lugano past a helpless Fernando Muslera.
The goal roused Uruguay and they came close with an Edinson Cavani header before Iniesta and Fabregas orchestrated Spain's second with Iniesta dragging defenders one way and Fabregas' instead passed to Soldado who coolly slotted home.
Spain relaxed in the second half but still controlled the game and almost scored a third in the 49th minute but Pedro narrowly failed to get a touch on Soldado's cross.
Neither side threatened seriously after that but Uruguay picked up a late consolation when Liverpool striker Luis Suarez curled home a free kick two minutes from time.
The game was the first to be played at the Arena Pernambuco in Recife and most of the locals in the 42,000 crowd were vociferously behind their Latin American neighbours.
However, Uruguay struggled to get out of their own half, particularly in a first half during which Spain had 78 percent of the possession, while Suarez and Cavani rarely threatened Iker Casillas in the Spanish goal.
The win takes Spain's unbeaten run to 23 matches.
"We couldn't relax for a moment even when we were winning 2-0. When they scored some doubts set in," Soldado told Telecinco.
"They were pushing forward and we were suffering in the final stages and it was a shame that we didn't manage to take some of our chances.
"We are very happy because we were able to beat a very tough opponent."
Spain's next game is against Tahiti on Thursday, while Uruguay will face Nigeria on the same day.
Nigeria play Oceania champions Tahiti in the other Group B game in Belo Horizonte on Monday.
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