Davydenko, who reached the quarter-finals in Dubai in his last outing this year, took his tally of victories to 10 for the season and improved his record against Mathieu to 7-4.
The Russian hit five aces and won 77 per cent of his first service points over the course of the match, which he wrapped up in just under an hour and a half.
Davydenko, now ranked 42 by the ATP, next plays Juan Martin Del Potro, who received a first-round bye at the Indian Wells Tennis Garden.
Tommy Robredo, ranked 69 in the world, was ousted by Marinko Matosevic, who won 7-5 6-2.
Matosevic, placed 16 spots higher in the world rankings than the Spaniard, becomes the fourth Australian into the second round, after Bernard Tomic, Lleyton Hewitt and Matthew Ebdon, the latter beating Andrey Kuznetsov 6-3 4-6 6-4 on the same day.
American James Blake cheered the home crowd with a 6-3 6-4 win over Dutchman Robin Haase.
It was a regulation victory for the former world number four, now 99, that was completed in just under an hour. He next faces Jo-Wilfried Tsonga in a clash sure to prick the interest of the Californian crowd.
US Open champion Andy Murray's first opponent will be Evgeny Donskoy after the Russian downed Tatsuma Ito of Japan 6-2 6-1 in his first-round clash.
And Novak Djokovic, the top seed, will meet Fabio Fognini in his opener, the Italian beating Slovenia's Aljaz Bedene 6-4 6-3 for the privilege.
BNP Paribas Open results
Lu Yen-Hsun (Taiwan) beat Tim Smyczek (U.S.) 2-6 6-2 6-2
Bobby Reynolds (U.S.) beat Benjamin Becker (Germany) 6-3 3-6 6-4
Michael Llodra (France) beat Daniel Munoz (Spain) 7-5 6-3
Daniel Gimeno-Traver (Spain) beat Lukas Lacko (Slovakia) 6-1 6-4
Fabio Fognini (Italy) beat Aljaz Bedene (Slovenia) 6-4 6-3
Bjoern Phau (Germany) beat Alejandro Falla (Colombia) 7-6(1) 6-2
James Blake (U.S.) beat Robin Haase (Netherlands) 6-3 6-4
Nikolay Davydenko (Russia) beat Paul-Henri Mathieu (France) 7-6(1) 6-2
Ivo Karlovic (Croatia) beat Jack Sock (U.S.) 3-6 7-6(8) 6-2
Carlos Berlocq (Argentina) beat Santiago Giraldo (Colombia) 6-0 2-6 7-5
Evgeny Donskoy (Russia) beat Tatsuma Ito (Japan) 6-2 6-1
Albert Ramos (Spain) beat Horacio Zeballos (Argentina) 6-3 6-3
Matthew Ebden (Australia) beat Andrey Kuznetsov (Russia) 6-3 4-6 6-4
Pablo Andujar (Spain) beat Steve Johnson (U.S.) 2-6 6-1 6-4
Philipp Petzschner (Germany) beat Dmitry Tursunov (Russia) 6-4 6-4
Marinko Matosevic (Australia) beat Tommy Robredo (Spain) 7-5 6-2