Djokovic, who reached the last four Flushing Meadows final and won it all in 2011, needed just 88 minutes to dismiss the veteran Frenchman on a gusty Arthur Ashe Stadium court.
The Wimbledon champion broke Mathieu to open the match and never eased off the gas as he swept through the last seven games to clinch an emphatic win.
"It was very windy but I was able to adjust. I used my serve efficiently, getting them in," said the Serb, who pounded in 75 per cent of his first serves including 13 aces without a double fault.
Djokovic joked about how his coach, Boris Becker, whose big serve in his playing days brought him the nickname "Boom Boom," would not be impressed.
"Thirteen aces he used to make in one set," joked Djokovic. "It's not a big number for him, but big for me. Glad it was working."
Most other leading seeds also stayed on course at the year's last Grand Slam.
Raonic, who became the first Canadian man to reach a Grand Slam semi-final at Wimbledon in July, produced a muscular display at the US National Tennis Center.
Along with his 26 aces, Raonic fired 64 winners in the three hour scrap with the German qualifier.
Raonic will next meet Victor Estrella Burgos of the Dominican Republic who beat Croatia's Borna Coric 7-6 (2) 4-6 6-4 6-2.
Ninth seed Jo-Wilfried Tsonga of France breezed by Aleksandr Nedovyesov of Kazakhstan 6-3 6-4 6-4 and big-serving American John Isner, the 13th seed, beat German Jan-Lennard Struff in straight sets.
Philipp Kohlschreiber, the 22nd seed, had an even quicker time booking a place in the third round as France's Michael Llodra retired after dropping the first set 6-2, due to an ailing elbow.
Those retirements raised the number of withdrawals in the men's draw to eight not yet halfway through the second round.
Hard-hitting American Sam Querrey limited his time spent on court against a healthy Guillermo Garcia-Lopez with his racket, beating the 28th-seeded Spaniard 6-3 6-4 6-4.
"If I keep playing like I played today I will keep going in the right direction and hopefully get back up in the top 20," said Querrey, who has slipped to 57th in the rankings.
Querrey won the dubious prize of facing Djokovic in the next round.
"Sam is one of the top Americans," noted Djokovic. "He has a big serve on any surface. If he serves well, he is dangerous."
US Open results
8-Andy Murray (Britain) beat Matthias Bachinger (Germany) 6-3 6-3 6-4
1-Novak Djokovic (Serbia) beat Paul-Henri Mathieu (France) 6-1 6-3 6-0
Pablo Carreno (Spain) beat Benoit Paire (France) 6-1 6-4 3-6 6-3
9-Jo-Wilfried Tsonga (France) beat Aleksandr Nedovyesov (Kazakhstan) 6-3 6-4 6-4
13-John Isner (U.S.) beat Jan-Lennard Struff (Germany) 7-6(5) 6-4 6-2
Sam Querrey (U.S.) beat 28-Guillermo Garcia-Lopez (Spain) 6-3 6-4 6-4
10-Kei Nishikori (Japan) beat Pablo Andujar (Spain) 6-4 6-1 (Andujar retired)
22-Philipp Kohlschreiber (Germany) beat Michael Llodra (France) 6-2 0-0 (Llodra retired)
5-Milos Raonic (Canada) beat Peter Gojowczyk (Germany) 7-6(4) 5-7 6-4 7-6(3)
Andrey Kuznetsov (Russia) beat 31-Fernando Verdasco (Spain) 6-3 4-6 4-6 7-5 6-3
Nick Kyrgios (Australia) beat Andreas Seppi (Italy) 6-4 7-6(2) 6-4
Victor Estrella (Dominican Republic) beat Borna Coric (Croatia) 7-6(2) 4-6 6-4 6-2
16-Tommy Robredo (Spain) beat Simone Bolelli (Italy) 5-7 6-7(5) 6-4 6-3 6-2
- Sports & Recreation
- Pablo Andujar
- Milos Raonic