The ex-Manchester United and Fulham man - who was sent off late on in Everton's 4-0 win over AEK Athens - netted either side of the break to heap more misery on struggling Blackburn Rovers.
Saha then turned provider to allow defender Joseph Yobo to put the nail in the coffin for Rovers as he poked home a third on the hour mark.
After a slow start to their Premier League campaign, David Moyes' men were looking to make amends and could have taken the lead inside a minute but defender Johnny Heitinga's effort flew wide.
Blackburn remained on the back foot and Chris Samba was forced to block a shot from Leon Osman, while Saha nodded wide of Paul Robinson's goal.
The visitors almost stunned the Toffees with a rare venture forward as El Hadji Diouf's long-range effort tested the alertness of keeper Tim Howard.
But it didn't take Everton long to break the deadlock as Leighton Baines' free-kick found Saha in space and he volleyed home past Robinson.
Samba and Everton winger Steven Pienaar traded shots as the game opened up, but it was Blackburn who finished the half the stronger with Morten Gamst Pedersen worrying the home rearguard.
Saha all but put the game to bed eight minutes into the second half as he headed a pinpoint Marouane Fellaini cross past the despairing dive of Robinson.
Saha and Osman both forced smart saves from the England keeper before Yobo added the third in the 58th minute when he prodded home Saha's flick.
Blackburn hit back with teenager David Hoilett trying his luck and Diouf stinging the palms of Howard.
But Everton looked more likely to add to their tally at the other end with Fellaini firing wide and Pienaar bringing out the best in Robinson late on.