The hosts took the lead on 21 minutes at Goodison Park, as Lewis Gibson finished at the back post from an Antony Evans free-kick.
Three minutes after the break, Rovers were level through Joe Rankin-Costello, who swivelled in the penalty area and fired into the bottom corner.
Everton regained the lead on 76 minutes after Simms was played in by Anthony Gordon before finishing beyond Joe Hilton.
Everton: 20 Sep v Brighton (A)
Blackburn: 23 Sep v Spurs (H)