Aberdeen and Ross County are both still waiting for their first goal of the season, with the home side particularly wasteful at Pittodrie.
County stood toe to toe with Craig Brown's side in an even first half.
But it was the Dons who were in control after the break and Gavin Rae ought to have found the target with an unchallenged header in front of goal.
Scott Vernon also passed up a great chance as County survived to start their top-flight life with two draws.
It stretches the Dingwall side's unbeaten league run to 36 games - a full calander year - and left frustrated much of a large crowd boosted by the Sell Out Saturday campaign designed to compensate for the financial loss of Rangers to Scottish Premier League clubs.
The attendance of 14,000 was 8,000 short of capacity but 4,000 more than watched the Dons' opener last season.
Little has changed on the field of play, however - as that too ended goalless, although an unchanged Aberdeen continued to show the kind of promise they displayed last weekend as they ran the reigning champions close before a late mistake by goalkeeper Jamie Langfield handed Celtic victory.
The Aberdeen support appeared buoyed by that promising display in Glasgow and their anticipation heightened as Stephen Hughes fired into the side netting from just inside the County penalty box after a clever Vernon flick set up the midfielder.
Sam Morrow, chosen to start for County in place of Russell Duncan, was causing problems and his presence alone was enough to distract a Dons defence that looked so comfortable at Celtic Park as a cross found its way to Martin Scott.
However, the midfielder back at Victoria Park on loan from Hibernian sliced his drive wide from 15 yards.
Hughes powered into the visitors' box but fired weakly straight at goalkeeper Michael Fraser, while County's Richard Brittain and the Dons' Jonny Hayes sent low drives just wide from distance.
Aberdeen started the second half brightly and three men with Scotland experience ought to have put the home side ahead.
Hughes' clever ball put Gary Naysmith clear down the left and the full-back's cross found Rae rising unmarked 12 yards out, but the veteran midfielder's downward header bounced clear of the far post.
As with the first half, County managed to stifle the home side's early momentum and the home side suffered another blow when winger Niall McGinn was stretchered off after the summer signing went down heavily after a challenge with Grant Munro.
County were rarely threatening but were almost handed the opener by a poor clearance by Langfield that was pounced upon by Duncan.
However, the goalkeeper made amends, stopping Brittain's low 16-yard drive with his legs.
Vernon missed a sitter when found by a free-kick by McGinn's replacement, Ryan Fraser, but the striker passed the ball straight into goalkeeper Fraser's arms.