Murray, who had to come from a set and a game down to beat Pablo Andujar on Wednesday, made a similarly laboured start against Sousa.
However, having gone a break down early in the first the number two seed rallied with two breaks of his own to secure the set.
The second set was a far more comfortable affair as Murray took one of his two break points to set up a quarter-final clash with Gilles Simon, who secured his place in the last eight with a 6-4 6-3 win over American lucky loser Donald Young.
Ferrer has not lost to a compatriot other than Rafa Nadal - the top seed at this tournament - for 40 matches, a run stretching back to the 2010 US Open.
It was Ferrer's 251st hard court win, following his milestone victory over Mikhail Kukushkin in his opening match at the Abierto Mexicano Telcel.
And the in-form Alexandr Dolgopolov also won through with a 6-3 6-4 victory over Jeremy Chardy of France.
Ukrainian Dolgopolov, who reached the final in Rio de Janeiro, faces big-serving Ivo Karlovic in the next round, following the Croat's 7-6(4) 6-2 win over Dudi Sela.
Acapulco International results
2-Andy Murray (Britain) beat Joao Sousa (Portugal) 6-3 6-4
4-Grigor Dimitrov (Bulgaria) beat Marcos Baghdatis (Cyprus) 6-1 6-4
6-Gilles Simon (France) beat Donald Young (U.S.) 6-4 6-3
7-Ernests Gulbis (Latvia) beat David Goffin (Belgium) 6-1 3-6 7-6(5)
Ivo Karlovic (Croatia) beat Dudi Sela (Israel) 7-6(4) 6-2
Alexandr Dolgopolov (Ukraine) beat Jeremy Chardy (France) 6-3 6-4