The world number six, making his debut in Dubai, saved seven break points in the first set before taking full advantage of Paire's troublesome right knee and prevailing in 81 minutes.
Top seed Nishikori will next take on Polish qualifier Hubert Hurkacz who beat another Frenchman in Corentin Moutet 6-3 7-5.
The seeds continued to tumble as Daniil Medvedev and Marin Cilic crashed out in the opening round.
World number 113 Ricardas Berankis stunned eighth seed Medvedev 6-3 6-3 while Frenchman Gael Monfils knocked out third seed and former U.S. Open champion Cilic 6-3 4-6 6-0.
The Lithuanian qualifier, who won his 11th ATP Challenger title last month in Rennes, faces Denis Kudla next after the American rallied past Matteo Berrettini 2-6 7-5 7-5.
Twice finalist Tomas Berdych faced a stern test from lucky loser Ilya Ivashka before prevailing 6-4 4-6 7-6(4) in two hours and 30 minutes.
