Race leader Primoz Roglic’s withdrawal meant Thibaut Pinot (Groupama-FDJ) started the day with a 10-second lead as he tried to become the first French winner of the race in 13 years.
But it was Colombian Martinez who took victory as he finished second on the stage and pipped Pinot by 29 seconds, with Guillaume Martin (Cofidis) coming third overall.
"This morning they told me Roglic wouldn’t start, so I knew the race would be hectic from the beginning," said Martinez.
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"My team worked very well for me in the first part and I was able to save strength for the finale and go for the win. I was at the limit but I was determined to make it to the finish. It’s one of the biggest race in the world and to be able to win this, coming from Colombia, makes me very happy."
Kuss attacked with around 9km remaining and pulled clear to secure a third stage win for Jumbo-Visma, who, as well as losing Roglic from the race, also saw Steven Kruiswijk crash out on stage four.
The riders opted to neutralise the opening descent of the final stage in protest at the road conditions the previous day, which Tom Dumoulin described as "disgraceful".
When the action did start, Pavel Sivakov (Team Ineos) and Julian Alaphilippe (Deceuninck-QuickStep) pulled away from an early breakaway group.
Sivakov recovered from a nasty fall to re-join Alaphilippe, but the leading duo were caught with around 23km remaining.
Martinez was among the riders to come to the front and he managed to maintain a winning advantage over Pinot in an exciting finale.
As Kuss surged clear at the base of the final climb, Pinot attacked from the group behind and trimmed Martinez’s virtual lead to 12 seconds.
However, Martinez finished strongly and crossed the line in second place to secure overall victory.
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