Djokovic, playing in the late night match, cruised to a 6-1 6-0 victory over Lukas Rosol.
Three-time Miami champion Djokovic seized upon five of his seven break point chances to ease into the third round with a 53-minute victory.
“It is a great start,” said the Serb who stepped on court following a three-hour rain delay and a 27-minute blackout.
“After Indian Wells, I tried to rest. There are different conditions here, but tonight was perfect for tennis. I enjoyed every moment of it and I love this court.”
But former US Open champion Del Potro suffered a surprise 7-6 6-1 loss to Germany's Tobias Kamke.
The towering Argentine had two set points in the opening set but lost his way just a week after making the men's final at Indian Wells.
"He didn't play obviously his best tennis," said Kamke. "But still I think I did a good job and pretty satisfied with that."
Spain's David Ferrer, the men's third seed, had an easier time. He won in a walkover when Russian qualifier Dmitry Tursunov pulled out and will face Fabio Fognini for a place in the last 16 after the Italian beat Michael Llodra of France 6-4 6-1.
Seventh seed Janko Tipsarevic eased into the third round with a straight-sets defeat of Dudi Sela.
The Serb, ranked ninth in the world, converted four of his five break points to win 6-2 6-4 while saving five of Israeli qualifier Sela's six.
He will next face giant South African Kevin Anderson, ranked 26th, after his 6-3 7-6(4) win over Horacio Zeballos of Argentina.
Tommy Haas was made to work for victory over Igor Sijsling as the German triumphed 6-0 5-7 6-3.
Germany’s 15th seed Haas took a first-set bagel but dropped serve for the first and only time late in the second set. Haas broke his opponent again in the third to close out victory in just under an hour and a half.
It was the eighth time Haas reached the third round at Crandon Park. He will face Alexandr Dolgopolov after the Ukrainian beat Nikolay Davydenko 6-2 6-3.
Japan’s Kei Nishikori cruised into the third round with a 6-3 6-3 win over Victor Hanescu of Romania.
The 13th seed broke Hanescu five times to claim victory in an hour and 20 minutes.
Nishikori will face Belgium’s Xavier Malisse in the third round after he beat 22nd seeded Frenchman Jeremy Chardy 6-3 6-2.
Miami Masters second-round results:
Somdev Devvarman (India) beat Edouard Roger-Vasselin (France) 4-6 6-4 7-5
1-Novak Djokovic (Serbia) beat Lukas Rosol (Czech Republic) 6-1 6-0
26-Kevin Anderson (South Africa) beat Horacio Zeballos (Argentina) 6-3 7-6(4)
11-Gilles Simon (France) beat Lleyton Hewitt (Australia) 6-3 6-3
Tobias Kamke (Germany) beat 5-Juan Martin Del Potro (Argentina) 7-6(5) 6-1
19-Alexandr Dolgopolov (Ukraine) beat Nikolay Davydenko (Russia) 6-2 6-3
James Blake (U.S.) beat 24-Julien Benneteau (France) 6-2 6-3
7-Janko Tipsarevic (Serbia) beat Dudi Sela (Israel) 6-2 6-4
Albert Ramos (Spain) beat 12-Juan Monaco (Argentina) 6-2 4-6 6-3
32-Fabio Fognini (Italy) beat Michael Llodra (France) 6-4 6-1
Jurgen Melzer (Austria) beat 31-Marcel Granollers (Spain) 6-3 6-4
Grega Zemlja (Slovenia) beat 23-Florian Mayer (Germany) 6-3 7-6(3)
3-David Ferrer (Spain) beat Dmitry Tursunov (Russia)WO
15-Tommy Haas (Germany) beat Igor Sijsling (Netherlands) 6-0 5-7 6-3
13-Kei Nishikori (Japan) beat Victor Hanescu (Romania) 6-3 6-3
Xavier Malisse (Belgium) beat 22-Jeremy Chardy (France) 6-3 6-2