Two goals from Rodrygo after 33 and 43 minutes, a third from Marco Asensio 10 minutes into the second half and a goal from Karim Benzema in the 81st minute, gifted Carlo Ancelotti's side the 35th league title in the club's history.
Second-placed Sevilla is 17 points adrift of Real Madrid with four games left, while FC Barcelona, who has five games still to play, is 18 points off the pace.
Ancelotti rested nine of the 11 players who faced Manchester City in the Champions League last Tuesday, with only Luka Modric and Thibaut Courtois keeping their places ahead of next week's European return leg.
Rodrygo's opening goal came in the 33rd minute when he received a cross from left back, Marcelo and beat two defenders before scoring with a low shot across Espanyol keeper Diego Lopez.
The second goal came after Mariano Diaz pressured the Espanyol defense into an error as they looked to play the ball out from the back. Rodrygo collected the ball and scored with a shot that was tight against the post.
Marco Asensio made it 3-0 in the 55th minute when he slipped through to finish off a counter-attack by Eduardo Camavinga.
Camavinga, Modric and Mariano were replaced by Karim Benzema, Toni Kroos and Isco on 60 minuutes and Isco thought he had added a fourth with 20 minutes left to play only for it to be ruled out for offside.
However, Benzema did net a fourth with a typical first-time finish following a move between Vinicius Jr and Isco.
On a personal level, the win means that Ancelotti has now led clubs to league titles in Spain (Real Madrid), Italy (AC Milan), England (Chelsea), France (Paris Saint Germain) and Germany (Bayern Munich).
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