Cobb smashed 107 and O'Brien hit 104 in an opening partnership of 193 that was the cornerstone of the Foxes total of 289.
It proved too much for the Gladiators, who never recovered from a nightmare start to their innings and were dismissed for 174 to lose by 115 runs, with Cobb following up his heroics with the bat by taking three for 34
Cobb, the Foxes one-day captain, and O'Brien, on his one-day debut for the county, gave an electrifying display after the Gladiators won the toss and decided to field first.
They raced to a 50 partnership off 35 balls with O'Brien hitting five boundaries and Cobb four. By the end of the power play it was 63 for no-wicket, and the runs continued to flow.
Cobb was first to his half century off 47 balls having hit a huge six off David Payne. O'Brien soon followed, reaching his 50 off 44 balls,and both batsmen then put their foot on the accelerator.
They pierced the field at will with O'Brien offering the only chance when he was dropped in the deep off Benny Howell on 86. He reached his century off 79 balls with a six and 12 fours before holing out to long off in the 27th over.
Cobb went to his century off 89 balls with eight fours and three sixes. But he too perished going for another big hit skying a catch off Ed Young. After that wickets fell at regular intervals with only Matt Boyce (28) offering much resistance as the Foxes lost their last eight wickets for 74 runs in 10 overs with Payne taking three for 45.
The Gladiators made a disastrous start to the runs chase slumping to 44 for five in 10 overs with both Michael Klinger and Chris Dent run out by some sharp fielding from the Foxes.
Then Cobb came on to bowl his off-spin and capped a man of the match performance by taking the wickets of Ian Cockbain, Gareth Roderick and Will Gidman to finish with competition best figures of three for 34. Robbie Williams also took three for 34 with the Foxes winning the game with 35 balls remaining.