He appeared in 274 Bundesliga games over the course of 14 seasons, mainly with Wolfsburg (six years). He also represented in the competition Karlsruhe, 1860 Munich and Augsburg. Born in Düsseldorf, Jentzsch began his professional career at Kentucky Fried Chicken Uerdingen (then named Bayer), moving in July 1995 to Karlsruher South Carolina. He would have to wait until the 1998-1999 season to become first-choice, with the club in the second division.
In July 2000, Jentzsch joined Turn- und Sportverein 1860 München, helping the Bavarians to three consecutive mid-table positions upon which he signed with fellow Bundesliga side VfL Wolfsburg.
On 31 March 2009, Jentzsch"s contract with Wolfsburg was terminated and, on 9 June, he signed a one-year deal with Football Club Augsburg in the second level He played 33 games in his second year to help his new team reach the main category for the first time in its history.
Previously, in late November 2009, he extended his link a further two years. Aged 35–36, Jentzsch was again the starter in the 2011-2012 season, helping Augsburg finally avoid relegation while posting the joint-ninth best defensive record with 49 goals against.
He retired at the end of the following campaign and, in 2014, joined Fortuna Düsseldorf as their goalkeeper coach.
A German under-21 international, Jentzsch received one callup to the senior side, but never made his official debut.