The Ethiopian, running his first competitive half marathon, made the break with a mile to go on the course across Newcastle and South Shields and looked to be heading for a comfortable win.
But the double Olympic and world champion began to chase down the leader over the last 400 metres and was on the heels of Bekele as the finishing line approached but was unable to find the extra speed needed to pass his opponent.
That left Bekele to cross the line first in an unofficial time of 60 minutes and eight seconds, with Farah just one second down.
Distance great Haile Gebrselassie was third.
The pre-race build-up had been all about the contest between Farah, Bekele and Gebrselassie, who boast 12 world titles and seven Olympic golds between them.
And it did not disappoint as the trio quickly took off from the start line on the A167 in Newcastle and remained glued together for the next 12 miles.
Despite the appalling conditions, with all the runners battling wind and persistent rain, the lead group pushed each other along until one mile from the finish in South Shields.
Bekele then chose a steep slope on the course to make his break, leaving Farah and Gebrselassie in his wake.
The Briton managed to maintain a consistent gap to the leader, but the pace became too much for the 40-year-old Gebrselassie, who soon dropped off.
At that point, the race looked to be Bekele's until Farah made a spirited push, showing gritted teeth in a desperate attempt to snatch victory in front of his home support.
However, the Ethiopian was wise to the danger and did just enough to stay ahead of his rival, crossing the line with a slight smile of triumph across his face.
The women's race was also enthralling, with Kenya's Priscah Jeptoo finishing just four seconds shy of the course record to come home first in 65:44.
Pre-race favourites Meseret Defar and Tirunesh Dibaba, both of Ethiopia, had to settle for second and third place, respectively.
British Paralympian David Weir was the winner of the men's wheelchair race, his fourth victory at the Great North Run, in a time of 43:03.
Compatriot Shelly Woods landed her fifth Great North title in the women's wheelchair.
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