Serb Djokovic fell to another promising youngster, Bulgaria's Grigor Dimitrov, in the second round of the Masters event on Tuesday but Nadal showed why he has the best record on clay in the pro era with a clinical display.
The Spanish world number five, who has won four titles since his return from a seven-month injury layoff in February, delighted the home support at the Magic Box arena with some brilliant shotmaking.
He broke the 23-year-old Paire once in each set and will meet unseeded Russian Mikhail Youzhny for a place in the last eight. Youzhny survived a second set comeback from 11th seed Nicolas Almagro to beat the Spaniard 7-6(4) 4-6 6-2.
"I am taking things day by day and I don't know if I am in perfect shape or not," Nadal, who could meet great rival Roger Federer in the semi-finals, said in an interview with Spanish television broadcaster La Sexta.
"The important thing is that I am here in Madrid competing again after seven months out injured," added the 26-year-old.
Fourth seeded David Ferrer had little trouble in following compatriot Nadal into the last 16 with a comfortable 7-5 6-2 victory Uzbekistan's Denis Istomin.
Sixth-seeded Czech Tomas Berdych had to come back from a set down to get past Poland's Jerzy Janowicz 6-7 6-3 6-2, while Japanese 14th seed Kei Nishikori ousted Viktor Troiki of Serbia 7-5 6-2.
In a match dubbed "the battle of the veteran Tommies", 13th-seeded German Tommy Haas, 35, continued his winning run after his victory at the Munich event at the weekend with a 6-3 7-5 second-round success against 31-year-old Spaniard Tommy Robredo.
Second round results 15-Stanislas Wawrinka (Switzerland) beat Santiago Giraldo (Colombia) 6-3
4-David Ferrer (Spain) beat Denis Istomin (Uzbekistan) 7-5 6-2
Mikhail Youzhny (Russia) beat 11-Nicolas Almagro (Spain) 7-6(4) 4-6 6-2
7-Jo-Wilfried Tsonga (France) beat Robin Haase (Netherlands) 7-6(5) 7-6(2)
Kevin Anderson (South Africa) beat Juan Monaco (Argentina) 7-6(5) 3-6 6-4
5-Rafael Nadal (Spain) beat Benoit Paire (France) 6-3 6-4
13-Tommy Haas (Germany) beat Tommy Robredo (Spain) 6-3 7-5
14-Kei Nishikori (Japan) beat Viktor Troicki (Serbia) 7-5 6-2
6-Tomas Berdych (Czech Republic) beat Jerzy Janowicz (Poland) 6-7(3) 6-3 6-2