Farah, also world champion at 5,000m and 10,000m, beat Kenya's Micah Kogo.
The world record of 58:23 was set by Eritrea's Zersenay Tadese in the 2010 edition of the Lisbon race.
Farah's only world record is the two-mile indoor mark he set at the Birmingham Grand Prix last month.
He clocked a time of one hour exactly in winning 2014's Great North Run, becoming the first British man to win the North East's famous half marathon for 29 years.
Kenya's Kogo, the 10,000m bronze medallist from the Beijing Olympics in 2008, was one of six men lining up against Farah to have already run under 60 minutes for the distance.
There was also British success in the wheelchair races for David Weir and Shelly Woods who continued their preparations for next month's London Marathon, which also doubles as the IPC World Championships.