Germany’s Kohlschreiber emerged from his clash with his 18-year-old compatriot with a 6-2 6-4 win to set up a showdown with fourth seed David Goffin.
The 2007 and 2012 tournament winner told www.atpwordtour.com: “I’m very happy. A very solid start, a high-quality solid game from my side, and I’m very happy with the performance.”
Belgian Goffin eventually triumphed in a hard-fought battle with Italy’s Simone Bolelli, taking the deciding set 6-1 after the first two had gone to tie-breaks.
Third seed Roberto Bautista Agut lost just three games as he got the better of Radek Stepanek 6-0 6-3, and he will meet Victor Estrella Burgos in the last eight.
Burgos needed two hours and 20 minutes to edge past wild card Janko Tipsarevic 6-4 6-7 (1) 7-5 after saving a break-point at 5-5 in the final set.
Meanwhile, Pablo Andujar came through his first round match against Joao Souza 6-4 6-4 and will now face qualifier Gerald Melzer.
In the doubles, there was a 7-5 6-2 victory for Britain’s Andy Murray – top seed in the singles draw – and Jean-Julien Rojer over third seeds Raven Klaasen and Lukas Rosol, and they will meet Rameez Junaid and Adil Shamasdin in the last eight.
Junaid and Shamasdin booked their place after a ding-dong battle with Britons Colin Fleming and Jonathan Marray, who lost 14-16 in the match tie-break after failing to convert four match points.
But Jamie Murray and Australian partner John Peers, who are seeded two, raced to a 6-3 6-2 win over Burgos and Souza in just 36 minutes and will take on brothers Alexander and Mischa Zverev in the next round.