Bigham, one of the most sought-after performance engineers in cycling who also happens to be a world-class track rider, led from the start and was 2.1 seconds ahead with 750 metres (three laps) left, but Ganna reeled him in.
For Ineos Grenadiers road powerhouse Ganna, twice the road time trial world champion, it was consolation after Olympic champions Italy lost in the final of the team pursuit to Denmark on Saturday.
"Thanks to Dan for an amazing battle in this velodrome," Ganna said after claiming his seventh track world title, six of them coming in the 4km individual pursuit.
Aerodynamics guru Bigham was part of Britain's gold medal-winning team pursuit squad at last year's track worlds and is eyeing next year's Olympics in Paris.
Bigham's biological prowess, combined with his aerodynamics expertise, helped him to break the Hour record last August, smashing the record of Belgium's Victor Campenaerts by travelling 55.548 kilometres in 60 minutes around a Swiss velodrome.
When he is not on his track bike, he spends his time developing kit that gives elite cyclists the marginal gains that can be the difference between success and failure.
He worked with the Denmark team pursuit squad that won the 2020 world title in Berlin in a then world record time.
Two months after his own Hour world-record ride he helped Ganna to take it off him, being part of the technical team behind the Italian's stupendous 56.792 kms in Grenchen.
On Sunday, Ganna again showed the benefits of having one of cycling's sharpest minds in his corner, although Bigham must have wished the Italian had taken the night off.
"We were training together a couple of months ago in Andorra with Ineos and Filippo said I'm not doing the IP this year, I'll make it a little easier," Bigham told reporters.
"Then today I saw his name on the start list. I sent him a message and he said, 'Yeah, I thought I would make it a bit of fun!' I thought game on!"
The pair shared a warm embrace after the race with Bigham saying they had a 'mutual respect' for each other's skills.
"That's my problem I guess, I'm always telling people what they're doing wrong and how they can do it better.
"But I ran him pretty damn close. With four laps to go the taps were open and I'm all out and it's then whatever I've got and I just didn't quite have it."
It was Italy's first track gold of this year's World Championships and Lotte Kopecky then provided Belgium's first when she won the elimination race, producing a powerful sprint to beat France's Valentine Fortin, with Jennifer Valente of the United States in third place.
