Everton were targeting their third victory of the summer but Baptiste and Caton’s second-half goals secured victory for the hosts.
Pienaar, on his return to the Toffees, thought he had teed up Marouane Fellaini for the opener, only for the Belgian’s header to be ruled out for offside.
Naismith combed well with Nikica Jelavic in attack, but the hosts were also causing problems with Gerardo Bruna twice testing Toffees ‘keeper Jan Mucha.
And they were rewarded for their efforts in the second half when Baptiste rose highest at a corner to bury a powerful header past Tim Howard, who replaced Mucha at the break.
Leon Osman and Seamus Coleman had chances to level either side of a penalty appeal when Ross Barkley’s effort hit Craig Cathcart.
But the Seasiders had the final word four minutes from time when Caton raced onto Curtis Thompson’s ball over the top and steered the ball past Howard.