The hosts were the first to threaten the opposition goal when Diogo Figueiras latched on to a fine defence-splitting pass before shooting from the edge of the box, only for Diego Marino to make the save.
Rakitic then narrowly fired over with a volley before the hosts did eventually double their advantage four minutes before the break, Kevin Gameiro receiving the ball inside the box and picking out the top corner with an accomplished finish.
Gameiro had a chance to double his personal tally for the afternoon just eight minutes after the restart when he latched on to a free kick, but he couldn't beat Marino with his strike.
The French striker wouldn't have to wait much longer for a second, however, as Sevilla were awarded another penalty in the 65th minute courtesy of a Stefan Mitrovic handball.
Gameiro stepped up to take it and made no mistake from 12 yards, slotting his effort straight down the middle to make it 3-0.
Things got even better for Sevilla 10 minutes later as they extended their lead to four when Figueiras converted Reyes's pass from inside the area.
Valladolid pulled a goal back immediately through Javi Guerra's fine strike, but it wasn't enough to prevent his side losing for the first time in four games as Sevilla saw out the victory.