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.
Everton made three changes from the side that beat AEK in midweek, with Dutch defender John Heitinga making his home debut.
Russia winger Diniyar Bilyaletdinov was out with a groin strain, while Jo and Dan Gosling dropped to the bench to allow Saha and Leon Osman into the starting line-up.
Blackburn gave Spanish defender Michel Salgado his full debut in an otherwise unchanged side from the one that achieved the club's first league win of the season against Wolves last time out.
This had been Everton's worse start to a league season since 2004, with only one win in their opening four games prior to this match.
Their intent to correct that unwanted statistic was evident from the outset. First Osman saw a shot on the turn deflected inches wide, and then Steven Pienaar's cross was headed onto the roof of the net by Saha.
But the game deteriorated into a scrappy affair with far too many stoppages and a general lack of ideas and invention.
Heitinga was booked by referee Lee Mason after a two-footed tackle that enraged the recipient David Dunn.
However, after 22 minutes, Everton were in front. Leighton Baines fired in a free-kick from the left and Saha arrived at the near post to turn the ball past Robinson.
Blackburn responded with a couple of headers from Christopher Samba and a twisting run and shot from Dunn which was held by Tim Howard.
Robinson saved well from Pienaar, and then watched a Marouane Fellaini drive fly wide after a quick Everton break.
Dunn was next into the book for a late tackle on Jack Rodwell.
Rovers sent on Ryan Nelsen for Gael Givet in the centre of defence at the break, with teenager David Hoilett replacing Morten Gamst Pedersen on the left after 50 minutes.
But it was Everton who extended their lead soon after. Fellaini's cross sailed in from the right and Saha got above Pascal Chimbonda with ease to send his header wide of Robinson's dive.
The former Tottenham goalkeeper t hen needed to save superbly to keep out an Osman drive, but Everton soon got their third.
Baines' corner from the right after 58 minutes hit Nelsen and fell invitingly for Yobo to fire in from a couple of yards out.
Allardyce opted to give Jason Roberts some support up front just after the hour, sending on Croatian striker Nicola Kalinic in place of Salgado.
There was some fight still left in the visitors, El-Hadji Diouf cautioned for a foul on Fellaini and Hoilett seeing a low drive blocked by Howard.
Howard was at last called into action to save from Dunn and Diouf, while Everton sent on Jo to replace Saha with 16 minutes left.
Next on was Tony Hibbert in place of Tim Cahill, with Heitinga moving into central midfield.
Teenager Gosling took over from Osman with nine minutes left, by which time Everton were well on their way to a comfortable three points.