The Toffees pair are transfer targets for former boss David Moyes at Manchester United, but the Scot's Goodison Park successor Roberto Martinez had no hesitation in including them at Cardiff City Stadium.
There was no lack of commitment from the pair in a full-blooded contest, although Cardiff will unquestionably be the happier with the point after being penned back for long periods.
Kevin Mirallas wasted two great Everton chances and David Marshall brilliantly saved a deflected Nikica Jelavic header, while the visitors were left scratching their heads at how they were not awarded a first-half penalty for Gary Medel's rash challenge on Baines.
Cardiff created little; skipper Craig Bellamy took too strong a touch when rounding Tim Howard, with the Everton goalkeeper also beating out a Peter Whittingham corner.
There had been a spring in the step and a bite in the Cardiff challenges in the early exchanges as they looked to unsettle their visitors as they had Manchester City six days earlier.
It made for an uncompromising opening and the first moment of any true quality only arrived when Steven Pienaar's exquisite drag-back took three defenders out of the game, but Ross Barkley could not make the most of the chance.
Corners had played a key part in Cardiff's victory over Manchester City and they almost repeated the trick when Whittingham's inswinger almost caught Howard off guard, but the American recovered just in time to bat the ball away.
But Everton also proved dangerous at free-kicks, and Mirallas and Phil Jagielka ought to have done better from headed opportunities.
Mirallas also glanced wastefully wide when picked out by Jelavic's pint-point cross as Everton took a hold on proceedings.
Fraizer Campbell, the two-goal hero against City, was a peripheral figure and he inadvertently botched what would have been Cardiff's best chance as he controlled a through ball destined for Whittingham.
The hosts were having to cope manfully with sustained pressure, with Medel excelling in midfield, but the Chile international was extremely fortunate not to concede a penalty on 42 minutes.
The Bluebirds' record signing brought down Baines as he charged into the area, but referee Anthony Taylor somehow only awarded a goal-kick.
To compound Everton frustrations Marshall then made an incredible save to palm away Jelavic's header after it had deflected off Ben Turner to leave him wrongfooted.
Having been penned back for much of the first half, Cardiff opened the second stanza with greater attacking intent and were unfortunate that Kim Bo-kyung's outwitting of Jagielka ended with his pull-back going behind his onrushing team-mates.
At the other end Jelavic could only scoop over from Barkley's weighted pass before Fellaini clashed with Campbell.
The midfielder bundled the striker over as he advanced towards the Everton box and then appeared to lean his elbow into him as he got up, but no action was taken.
Cardiff thought they may sneak a winner when Bellamy raced onto a Kim pass, but his touch as he rounded the advancing Howard took him too wide of goal.
Mirallas then had a chance to redeem himself for his earlier misses as the impressive Barkley found him in the box, but he checked inside and the chance was lost to leave Martinez still awaiting his first win in charge.