It was a vastly improved display, even on the win over Aston Villa, but Jose Mourinho’s men stayed third in Champions League Group G behind Porto and Dynamo, who remained unbeaten.
Mourinho had targeted four points from the double header with Dynamo — the Stamford Bridge return is on November 4 — and would have been content with a point after losing at Porto last time out.
Yet Chelsea came close to returning from NSK Olimpiyskyi with more.
Hazard, restored to the starting XI, hit the post with an early shot, Cesc Fabregas felt he was sandwiched in the box but penalty appeals were dismissed, and Nemanja Matic beat three men before prodding wide.
There was a sense Chelsea had to take one of those first-half chances, but another followed when Willian — excellent against opponents he knows well following his spell at Shakhtar Donetsk — hit the bar with a curling free-kick.
Andriy Yarmolenko showed why he is coveted with some surging runs as Dynamo pressed forward in the second half, but it finished in a stalemate.
Chelsea will go to West Ham on Saturday with confidence restored but with work to do domestically and in Europe.
Hazard was omitted from Chelsea’s starting XI for last Saturday’s defeat of Villa, with Mourinho afterwards demanding the Belgium playmaker improve his workrate.
With Pedro injured, Hazard returned against a Dynamo side bidding to respond from a first loss in 38 Ukrainian Premier League games, 3-0 to Shakhtar last Friday.
He apparently heeded Mourinho’s message against a Dynamo side whose head coach is Sergei Rebrov, once of Tottenham and West Ham.
The hosts had lost just one of their last 10 European home games, recording seven wins, and Chelsea’s initial priority was to keep it tight.
But the Blues were on the attack for much of the opening 30 minutes.
Willian struck a tame shot straight at Olexandr Shovkovskiy and a Fabregas effort was blocked into the path of Hazard, whose strike across goal was tipped on to the foot of the far post by the 40-year-old goalkeeper.
Fabregas, who won his 100th Spain cap in Kiev last week, wanted a penalty for a challenge by Serhiy Rybalka.
So did Mourinho, who is appealing a fine and suspended one-match stadium ban imposed after being denied a penalty against Southampton earlier this month. The pleas were dismissed.
Afterwards the Chelsea boss said: “The referee was weak and naive with the penalty. I cannot understand what the referee behind the goal does because he doesn’t make a clear decision too. I see progress.
“We hit the post twice, had a good, solid, defensive performance against dangerous team. To lose this game would have been bad for us.”
Matic then drove at the Dynamo defence and might have scored.
Dynamo looked dangerous too and Domagoj Vida beat Kurt Zouma, playing out of position at right-back, before finding Vitaliy Buyalskiy, whose shot deflected wide.
Willian, who had scored free-kicks in four successive games prior to the Villa win, went close again with a 25-yard set-piece which struck the bar. Matic could not quite reach the rebound.
There were yet more chances. Fabregas shot weakly and Hazard had a shot blocked before Dynamo pressed. Yarmolenko teed up Derlis Gonzalez, but Asmir Begovic was equal to the shot and then parried clear a curling effort from the Paraguayan. Vida scooped an opportunity over, Gonzalez shot at Begovic, and Junior Moraes was unable to get on the end of a cross after a poor John Terry clearance. Willian curled just wide as it finished level.
Shovkovskiy, Danilo Silva, Khacheridi, Dragovic, Vida, Sydorchuk, Rybalka, Yarmolenko, Buyalsky (Garmash 82), Gonzalez, Kravets (Junior Moraes 78).
Begovic, Zouma, Cahill, Terry, Azpilicueta, Matic, Fabregas (Oscar 75), Ramires, Hazard, Willian, Costa.
Damir Skomina (Slovenia).