Two-times defending champion Djokovic needed just 53 minutes to race past Lukas Rosol in his opening match on Friday and although he was tested a little more by Devvarman, the world number one rarely needed to move out of second gear.
Devvarman managed just the one break point opportunity, in the final game of the match, but Djokovic was easily able to save it before serving out at the first attempt to set up a clash against in-form German Tommy Haas.
Earlier in the day, 15th seed Haas had produced a compact performance in blustery conditions to beat potentially tricky Alexandr Dolgopolov, seeded 19th in Miami, 6-3 6-2.
In perhaps the most exciting match of the day, Djokovic's Serbian compatriot Janko Tipsarevic continued his tentative return to form with a battling 4-6 7-6(5) 6-0 win over 26th seed Kevin Anderson.
Seventh seed Tipsarevic had not won a match since the Australian Open coming into Miami but weathered a storm in the opening couple of sets, including the second set tie-break where he found himself 2-4 down, before outlasting Anderson.
The south African completely collapsed in the final set, managing to find just seven points and failing to secure a single game as he helped Tipsarevic set up a fourth round clash with Gilles Simon, the French 11th seed a 6-4 6-4 victor over Grega Zemlja.
Third seed David Ferrer racked up his fourth victory over Fabio Fognini this year, knocking the Italian 32nd out of the tournament with a 6-1 7-5 win to earn himself a match against 13th seed Kei Nishikori. The Japanese player eased past Belgium's Xavier Malisse 6-2 7-5 to reach the last 16.
Round three results
1-Novak Djokovic (Serbia) beat Somdev Devvarman (India) 6-2 6-4
11-Gilles Simon (France) beat Grega Zemlja (Slovenia) 6-4 6-4
7-Janko Tipsarevic (Serbia) beat 26-Kevin Anderson (South Africa) 4-6 7-6(5) 6-0
15-Tommy Haas (Germany) beat 19-Alexandr Dolgopolov (Ukraine) 6-3 6-2
13-Kei Nishikori (Japan) beat Xavier Malisse (Belgium) 6-2 7-5
3-David Ferrer (Spain) beat 32-Fabio Fognini (Italy) 6-1 7-5
Albert Ramos (Spain) beat James Blake (U.S.) 6-4 2-6 7-5
Jurgen Melzer (Austria) beat Tobias Kamke (Germany) 6-7(3) 6-3 6-4