World No 33 Kohlschreiber eases past French qualifier Gleb Sakharov 6-4, 6-2, while wildcard Stefanos Tsitsipas is also through to the last 16 of the tournament.
ATP Dubai Duty Free Tennis Championships Day 1 updates: Baghdatis, Kohlschreiber and Bautista Agut through to second round
Marcos Baghdatis defeated Viktor Troicki 7-5, 6-2 in the first evening match on Centre Court on Monday to reach the second round of the Dubai Duty Free Tennis Championships.
Baghdatis, the 2016 finalist, exchanged early breaks with his Serbian opponent early in the first set before claiming the all-important second break in the 11th game. The 32-year-old Cypriot then served out the opening set to love.
After a tightly-contested opener, it appeared Troicki's resistance had been broken as Baghdatis claimed successive breaks of serve to race into a 4-0 lead en route to victory.
Baghdatis will take on either Filip Krajinovic or Thomas Fabbiano in the second round.
Kohlschreiber first to register win
Philipp Kohlschreiber was the first player to book his place in the Dubai Duty Free Tennis Championships second round on Monday, defeating French qualifier Gleb Sakharov 6-4, 6-2.
Kohlschreiber, the world No 33, claimed the only break of the first set in the fifth game before clinching the opener by serving to love.
The 34-year-old German then broke in the opening game of the second set, and although he handed the break straight back to Sakharov, he immediately regained his advantage in the third game.
Kohlschreiber, a quarter-finalist here last year, earned a double break to move 4-1 ahead before serving out the match to love.
Kohlschreiber will take on either Greek wildcard Stefanos Tsitsipas in the second round.
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Wildcard Tsitsipas progresses
Greek wildcard Stefanos Tsitsipas booked a second round meeting with Philipp Kohlschreiber at the Dubai Duty Free Tennis Championships after beating Mikhail Kukushkin 6-2, 6-7, 6-3 on Monday.
After comfortably seeing out the opening set in 37 minutes, Tsitsipas was forced into a decider after both players proved unshakeable on serve in the second set and Kukushkin won the tie-break at the third time of asking.
Tsitsipas reasserted his dominance during the latter stages of the decider with successive breaks, firstly in the seventh game and then in the ninth to seal victory.
Tsitsipas and Kohlschrebier's second round meeting will be the first match between the pair on the ATP Tour.
Bautista Agut too good for Mayer
Spain's Roberto Bautista Agut advanced to the second round of the Dubai Duty Free Tennis Championships with a 6-3, 6-4 win over Florian Mayer of Germany.
Bautista Agut, seeded third in Dubai this week, produced a stuttering performance but ultimately did enough to progress in one hour and 18 minutes.
The Spanish world No 23 was broken twice in the opening set, but three breaks of his own handed him the advantage. Bautista Agut broke the Mayer serve in the opening game of the second set and looked more solid in his own service games, until Mayer broke back to level the set at 4-4.
However, the German could not consolidate the break back and handed Bautista Agut the chance to serve out the match, which he did to love.
Bautista Agut will take on either Portugal's Joao Sousa or Frenchman Pierre-Hugues Herbert in the second round.
Hasse wins in three sets
Dutchman Robin Haase survived a scare from French qualifier Quentin Halys to reach the second round of the Dubai Duty Free Tennis Championships on Monday.
Haase, the world No 43, recovered from a break down against the 115th-ranked Halys in the final set to win 7-5, 2-6, 6-4 in the day's longest match so far at two hours and 15 minutes.
Haase will take on either top seed Grigor Dimitrov or Tunisian wildcard Malek Jaziri in the second round on Wednesday.