Robin Smith, scenting the chance of an England recall at Graeme Hick's expense, was also at his best in helping Hampshire to demolish Worcestershire, from whom Hick failed.
Irani made 124 from 99 deliveries and including three sixes and 11 fours, while Law was out for exactly 100, scored off 114 balls, to pave the way for a total of 361 for 7, Essex's highest against a first-class county in the competition. Law's century was his ninth of the summer.
The total proved well beyond Durham, despite a fighting century from their captain, Mike Roseberry. Their challenge ended in the 57th over when they were all out for 294.
Irani and Law took control after Durham had reduced Essex to 43 for 3 inside 12 overs. They shared a stand of 121 in 18 overs, a county record for the fifth wicket, and Irani and Robert Rollins put on 105 in 12 overs, a county best for the sixth wicket.
Smith was superb in scoring 158 from 151 balls with 21 fours and two sixes as Hampshire ran up 328 for 6 in their 60 overs to set up a 125- run win over Worcestershire at New Road.
Hick, whose England place is under threat, was leg before to Kevan James for a six-ball nought as Worcestershire were all out for 203 inside 54 overs.
Smith made a shaky start and survived one difficult chance behind before getting into gear. His second-wicket stand of 179 in 33 overs with Jason Laney laid the foundations for Hampshire's huge total. Worcestershire's reply was undermined by James taking three quick wickets.
Ian Salisbury, not required by England at Trent Bridge, achieved a rare distinction for a leg-spinner in the one-day game when he was named man of the match for his part in a 32-run victory by Sussex over Leicestershire at Grace Road. He took 2 for 23 and scored a 30 in 17 overs.
Phillip DeFreitas took the man of the match award in Derbyshire's two- wicket victory over Kent at Derby but heaped praise on the inexperienced Andrew Harris, who was nerveless after joining him with Derbyshire rocking on 228 for 8 chasing 252 for victory.
n The International Cricket Council failed at its meeting at Lord's last night to elect a successor to Sir Clyde Walcott as chairman when none of the three candidates, Jagmohan Dalmiya, Krish Mackerdhuj and Malcolm Gray, achieved the required two-thirds majority. A new vote will be taken at the end of Walcott's term in July next year.Reuse content