Bekele, the world record holder over 5,000 and 10,000, won in one hour nine seconds on his debut over the 21.08-km distance from Newcastle to South Shields, with Briton Farah one second behind in wet and windy conditions.
Multiple world and Olympic gold medallist Haile Gebrselassie of Ethiopia was third in 1:00:41, an over-40 world best, as the three athletes, who between them have won all the Olympic men's 10,000 titles since 1996, raced together for the first time.
Bekele attacked on a downhill section in the final 1.6 km to pull clear of Farah and Gebrselassie and although the Briton, renowned for his pace on the track, chased down his rival over the last 400 metres he found himself crossing the line in the unusual position of second.
Farah, who won the long distance double at the World Championships in Moscow last month having achieved the same feat at the London 2012 Olympics, had mixed feelings.
"It was a great race, a great finish. I thought when Kenenisa went with a mile to go that the pace was just ridiculous, I thought I could come back and close the gap slowly," said Farah.
"I managed to close it a little bit but you can't take away what Kenenisa has, he has great speed and it came down to the last 200m, right to the line.
"I am disappointed to finish second, but I didn't just finish second, I finished second to a great athlete. It was a great race and Haile did most the work."
Farah will now take a well-deserved holiday before turning his attentions onto running the full London Marathon next year, having raced half this year.
And the 30-year-old insists his outing at the Great North Run has definitely proved beneficial as he bids for a successful outing on London's roads.
"It definitely taught me a lot for London. My main preparation this year was the world champs, that was my main focus," he added.
"I only had two to three weeks for prepare for this. I will take my break, go on holiday and get ready for the London Marathon."
London marathon champion Priscah Jeptoo of Kenya won the women's race in 1:05:44, ahead of Ethiopia's world and Olympic distance champions Meseret Defar and Tirunesh Dibaba.