Sandaza gave the visitors the lead in the first half, breaking a ragged Kilmarnock defensive line to slot past Cammy Bell for his seventh goal of the season.
After finding Peter Enckelman in great form and seeing a Rory McKeown effort crash an effort off the crossbar, Killie finally found the net in somewhat fortunate circumstances just before half-time, as Steven Anderson's header found the corner of his own net following a deep Dean Shiels delivery.
But in the second half Sheridan grabbed his third goal in two games to give St Johnstone the lead, rounding Bell and finishing with aplomb following some slack defending.
The returning James Dayton was first to test Enckelman, driving a low effort which was coolly fielded by the former Aston Villa keeper.
That effort was immediately followed by a drive from Killie's other floating attacker, Shiels, whose powerful right-footed effort from 20 yards flew past the Enckelman's right-hand post.
Despite early Kilmarnock pressure, Sheridan almost gave the visitors the lead just after the quarter-hour mark, as Scotland international Bell denied the Irishman. Sheridan showed great pace to burst past Mohamadou Sissoko into the box before lashing a low drive which Bell did superbly to parry.
The Saints had the lead with their next foray forward. Two former Dundee United players combined superbly, with Robertson slipping the ball through to Sandaza who calmly slotted past Bell.
Kenny Shiels' men tested the strength of the woodwork as they chased an equaliser. McKeown surged forward from the left flank and launched a thunderous 30-yard effort which crashed off Enckleman's crossbar.
Paul Heffernan, already with five SPL strikes this season, went close to levelling the scores with 10 minutes to play until the break, firing just wide. And the same man was denied minutes later, as Enckelman managed to parry his low effort wide of the post.
But it proved a temporary reprieve. From the resulting Shiels corner Anderson's wayward header looped over the Saints keeper and into the corner of the net to give the home side a deserved, if fortuitous, equaliser.
Kilmarnock were back on the front foot immediately in the second half, through the unlikely attacking protagonist of James Fowler.
The versatile veteran lashed an effort just over the bar after the ball broke to him on the edge of the area, before forcing another super save from Enckelman as a second shot in five minutes was deflected towards the top corner.
Bell had to be at his best on the hour as Sandaza threatened to grab a brace. The burgeoning partnership between Sheridan and the Spaniard was evident again, as the Irish striker's cross found the head of his partner, but Bell stooped to parry away.
The provider turned beneficiary with 15 minutes to play. The livewire Sandaza capitalised on a woeful Mohamadou Sissoko pass to slip a pass to Sheridan, who rounded Bell and fired into an empty net despite a prohibitive angle.
Instead of carving open St Johnstone in search of an equaliser, things actually threatened to get worse for the hosts as a powerful, deflected drive from substitute Chris Millar flew just past the post and the visitors held on.