The Force India Formula One driver, in the number 19 Porsche, led the number nine Audi by just over two minutes at the 17 hour mark with the safety cars deployed for a fourth time.
Hulkenberg, who shares the car with Briton Nick Tandy and New Zealand's Earl Bamber, had arrived in Le Mans straight from the Canadian Grand Prix and will be heading to Austria after the weekend.
There had been little to separate the two German manufacturers, both part of the Volkswagen stable, as dawn rose over the Sarthe circuit.
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However, Marcel Fassler had to pit the number seven Audi shortly before 0700 local after a large part of bodywork flew off the car without warning.
That cost seven minutes for repairs and pushed the Swiss, who is chasing a fourth win with team mates Benoit Treluyer and Andre Lotterer, down to fifth.
Australian Mark Webber, the former Red Bull Formula One driver, was third in the number 17 Porsche he shares with New Zealander Brendon Hartley and Germany's Timo Bernhard after leading at the quarter distance.
Six hour report: Webber leads Le Mans for Porsche
Webber was handed a one-minute 'stop and go' penalty after the eight-hours mark for overtaking under yellow warning flags through a slow zone imposed around the Mulsanne corner following the third safety car interlude.
The safety cars came out for a fourth time around the 17 hour mark when Roald Goethe's Aston Martin crashed, with debris across the track.
Porsche had qualified one-two-three thanks to their lightning one lap pace but Audi looked just as quick in race trim.
The safety cars, three of them to cope with the long Le Mans lap, made their first appearance after the first hour when a three car collision dumped oil on the track at the first chicane.
There was a much longer safety car interlude at the end of the third hour, when Frenchman Loic Duval spun and hit the barriers in the number eight Audi at the Indianapolis corner.
Duval nursed the car back to the pits and it resumed the race only four minutes later, with the safety car leading for 45 minutes.
Denmark's retired nine times winner Tom Kristensen had waved the 83rd edition of the race away in bright sunshine on Saturday, watched by a crowd of around 250,000 spectators enjoying the festival atmosphere.
Audi are chasing a 14th win in 16 years with their diesel hybrid car but face a tough battle from 16 times winners Porsche, who returned with a full factory effort last year.
Porsche last won the race in 1998.