Australian Tomic started fairly strong and conjured three break points early on, but offered little resistance as the Scot warmed up in the match.
And Murray, who will leapfrog Roger Federer in the rankings if he goes all the way in Miami, did not have to go any higher than second gear to dispatch the out-of-sorts world number 45 in just 56 minutes.
Up next for the Olympic gold medallist will be 29th seed Grigor Dimitrov who won the opening set over Simone Bolelli before the Italian retired with the second all square after two games.
Sixth seed Jo-Wilfried Tsonga is also through, taking an opening-set tie-breaker before finishing a straight-sets job on Viktor Troicki 7-6(6) 6-3.
Fourth seed Tomas Berdych overcame a scare when he recovered from a set down to beat Daniel Gimeno-Traver 5-7 7-6(3) 6-2.
ATP MIAMI MASTERS - ROUND TWO RESULTS
4-Tomas Berdych (Czech Republic) beat Daniel Gimeno-Traver (Spain) 5-7 7-6(3) 6-2
14-Milos Raonic (Canada) beat Guillaume Rufin (France) 6-2 6-4
9-Marin Cilic (Croatia) beat Santiago Giraldo (Colombia) 6-2 7-6(6)
20-John Isner (U.S.) beat Ivan Dodig (Croatia) 4-6 7-5 7-6(5)
28-Mikhail Youzhny (Russia) beat Lu Yen-Hsun (Taiwan) 6-3 1-6 6-0
10-Nicolas Almagro (Spain) beat Guido Pella (Argentina) 6-0 6-3
29-Grigor Dimitrov (Bulgaria) beat Simone Bolelli (Italy) 6-4 1-1 (Bolelli retired)
2-Andy Murray (Britain) beat Bernard Tomic (Australia) 6-3 6-1
Thomaz Bellucci (Brazil) beat 21-Jerzy Janowicz (Poland) 7-6(5) 3-6 6-3
Jarkko Nieminen (Finland) beat 27-Martin Klizan (Slovakia) 6-2 6-2
6-Jo-Wilfried Tsonga (France) beat Viktor Troicki (Serbia) 7-6(6) 6-3
16-Andreas Seppi (Italy) beat Aljaz Bedene (Slovenia) 7-5 5-7 7-5
David Goffin (Belgium) beat 18-Philipp Kohlschreiber (Germany) 7-6(5) 4-6 6-2
17-Sam Querrey (U.S.) beat Lukasz Kubot (Poland) 4-6 6-3 6-3
8-Richard Gasquet (France) beat Olivier Rochus (Belgium) 7-5 6-2
- Sports & Recreation
- Simone Bolelli