A largely dour game sparked to life with Doran's breakaway goal and a thunderbolt of a strike from Tansey, which went in via a combination of the post and goalkeeper Craig Samson, to keep Inverness unbeaten.
Inverness made one enforced change to the team that triumphed 1-0 over Celtic last Saturday. Gary Warren dropped out through injury and Doran took his place. Manager John Hughes reshuffled the shape of his team, moving Ross Draper to centre-back and Danny Williams to central midfield.
Kilmarnock made changes from midweek's 1-0 win over Ayr in the Scottish League Cup. Tope Obadeyi and Robbie Muirhead were left out with Michael Ngoo and Craig Slater coming in.
The home side had the first chance of the game through Ryan Christie, fresh from his call-up to the Scotland Under-21 squad. He collected the ball from Doran about 30 yards from goal and let fly, the shot sailing wide.
McKenzie had a chance at the opposite end for Kilmarnock, seeing his shot blocked by Josh Meekings, before Billy McKay had the ball in the net but had it chalked off for handball.
Both sides were struggling to create chances, despite David Raven and Marley Watkins getting some joy down the left side.
Ngoo, a recent signing for the visitors, was an awkward customer for Inverness to deal with, his 6ft 6in frame difficult to get around for defenders needing to make an interception.
With 37 minutes on the clock the lull in play was interrupted by a burst forward by Graeme Shinnie, who bulldozed his way into the penalty area between Kilmarnock defenders. The ball broke to the returning Doran who curled his effort over the top of Samson's crossbar.
Hearts were in mouths briefly before the break for supporters of the home side as an attempted clearance nearly went wrong. Josh Magennis saw his shot blocked and Tansey attempted to clear, only to slice the ball backwards looping over Dean Brill's crossbar.
The first shot on target came four minutes into the second half and it was the hosts who went close. Shinnie cut inside off the left flank and fired a shot which Craig Samson parried just away from Doran.
Inverness were starting to move the ball about quicker and were a Ross Barbour header away from taking the lead. Raven's cross was landing on McKay's head at the back post until the intervention of the Kilmarnock right-back.
They went even closer moments later as Doran floated a left-footed cross to the back post which landed on top of the crossbar and had Samson worried.
Neither side had lost a game this season but it was Caley Thistle who were threatening more. Meekings met a Doran corner with a first-time shot that was well-blocked by Mark Connolly, before Watkins had a penalty shout waved away after falling under Manuel Pascali's challenge.
The deadlock was nearly broken by the most unlikely source after 70 minutes as Doran's cross floated to the back post was met by full-back Raven, who only has one goal for Inverness, but Samson got down well to keep out the header.
Doran finally made the breakthrough with 15 minutes to go, racing on to a McKay through-ball, beating Samson to it and sliding his shot underneath the Kilmarnock goalkeeper.
The hosts doubled their lead five minutes later, Tansey letting fly from 30 yards and seeing his effort rebound off the post, only to hit the back of Samson and go into the back of the net.