Though Goffin showed some resilience by staying in the set with a tough hold having saved a set point, he crumbled on the return as Federer quickly closed out the first set 6-2 after 34 minutes.
Goffin saved three match points to ask Dimitrov the serve it out, but he kept his composure to seal a famous win on his fifth match point, although he was given a helping hand as the Belgian dumped a simple-looking volley into the net.
Dimitrov defeated Jack Sock of the United States 4-6, 6-0, 6-3 in the second semi-final at London's O2 Arena.
Grigor Dimitrov triumphed in the final season tournament!
The sixth seed started where he left off by making a blistering start, winning the first three games. "But in the end, I was really happy about the way I played the match, I was really nervous towards the end of the match", Goffin said in his on court interview after the match.
The Belgian opened the match well, acing Federer twice, but he threw away a game point allowing his opponent to swoop in and claim the first game easily. I will need some days rest but I will be ready next week.
Grigor Dimitrov edges out David Goffin in Tour Finals thriller
Despite Goffin's upset win - and his victory over world number one Rafael Nadal earlier in the week - Dimitrov is a 4/9 favourite for that one having dismantled the Belgian 6-0 6-2 in their group-stage meeting on Wednesday.
"I'm just looking forward to some time off now, away from the match court, away from the pressure, then hopefully play well in Australia", the 36-year-old said.
Growing in confidence, the 26-year-old broke Federer's serve again at 1-1 in the third set as the Swiss, suddenly hesitant, struck a backhand out.
Goffin, 26, landed just 42 percent of first serves in the first set and made 20 unforced errors, struggling to find the bite and consistency he had enjoyed in beating Federer.
Play continued with serve, but the early break allowed Goffin to serve for and claim the second set 6-3. I was very composed and didn't let negative thoughts come to my head.
Jack Sock was the unlikeliest of players to make it thus far.
Goffin is 1-3 against Dimitrov, who has won all four of his matches this week and is playing perhaps the best tennis of his career. But this time, instead of seeing a fiery Sock comeback, Dimitrov stormed to a 6-0 second set victory, losing just nine points. I'm sure neither one of us is going to think about that.
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