The Yellow Submarine had enjoyed a decade of unprecedented highs following their team before the club's shock relegation from the top flight at the end of the 2011/12 season - having finished fourth the previous season.
After winning promotion back to the elite at the first attempt, Villarreal played their first home match back in the Primera Division - only for it to start badly.
Javi Guerra put Valladolid ahead after just four minutes before Giovani Dos Santos equalised with a penalty seven minutes before half-time.
There were few clear-cut chances in the second half and the game appeared to be heading for a draw only for Cani to intervene.
Espanyol came from behind to take all three points at home to Valencia and record their first win of the league season.
Helder Postiga scored his first goal for Los Che after 10 minutes, but Espanyol responded with headed goals from David Lopez and Christian Stuani to take a deserved lead, which they never really looked in danger of surrendering, before substitute Thievy Bifouma made sure of the points in the 89th minute.
Carlos Vela's 74th-minute effort ensured Real Sociedad avoided a surprise defeat at Elche.
Sociedad had perhaps come into this fixture feeling the effects of their Champions League play-off win at Lyon earlier in the week, falling behind to Ferran Corominas' second-minute strike and looking sluggish in the opening half.
Elche, who were roundly beaten at Rayo Vallecano last week, could not hold on for the three points, however, and Mexican striker Vela grabbed a share of the spoils for Sociedad.