Davydenko has never played with much conviction on the lush lawns of south-west London and he seemed set for another early exit as Anderson surged into a two-set lead on Court One.
But the 29-year-old's pedigree is undeniable, as he proved by winning the ATP World Tour finals on his last visit to London in December, and he eventually managed to subdue the 6ft 8in big-server from Johannesburg.
Davydenko, a former French and US Open semi-finalist, had failed to make it past the first round on five of his previous eight visits to Wimbledon, but he could surpass his best effort, reaching the fourth round in 2007, if he continues to play with such determination.
Anderson took the first set impressively and then swept Davydenko aside in the second set tie-break.
With Davydenko looking completely out of sorts, it was no surprise to see Anderson break in the third set and take a 4-2 lead.
But Anderson was unable to serve out the match and this time Davydenko took control of the tie-break to pull a set back.
It proved the turning point. Davydenko was starting to get into his rhythm and took the fourth set as well after breaking at 6-5.
The final set was a gruelling affair but it was Davydenko who held his nerve to clinch a dramatic win.