Louis Saha scored after 22 and 54 minutes and then defender Joseph Yobo grabbed the third for the hosts, punishing poor defending at a corner after the impressive Paul Robinson had denied the France striker a hat-trick goal.
David Moyes' side had endured a slow start to the campaign, seemingly suffering a hangover from last season's FA Cup final defeat to Chelsea. But the Toffees appear to be back on track after following Thursday's 4-0 Europa League rout of AEK Athens with another fine win and clean sheet at Goodison Park against a disappointing Rovers side who were looking to haul themselves out of the relegation zone.
While Moyes' worries look to be easing, Rovers boss Sam Allardyce must be seriously concerned now about his side, who have won just one league game all term and were feeble for much of this clash.
Saha opened the scoring when he volleyed home a Leighton Baines free-kick and added a second with a fine header from Marouane Fellaini's cross.
Everton then grabbed a third when Baines' corner from the right struck Ryan Nelsen and fell invitingly for Yobo to fire in from close range.