Third-tier Dresden missed the 2013-14 DFB-Pokal campaign for persistent crowd trouble, which came to a head when their supporters set off flares and caused damaged in a second-round clash against Hannover the season prior.
But Dresden produced one of the shocks of the round thanks to goals from Justin Eilers and Nils Teixeira on home soil at the Glucksgas Stadion.
Schalke - third in the Bundesliga last season - were overwhelming favourites heading into the match but they soon found themselves trailing after Felipe Santana conceded a 24th-minute penalty.
The Brazilian defender was punished for a mistimed challenge on Luca Durholtz and Eilers stepped up to convert the spot-kick.
It got worse for the visitors just four minutes into the second half as defender Teixeira doubled Dresden's advantage.
Joel Matip's attempted clearance fell to the feet of Teixeira, who volleyed low into the bottom corner.
Schalke did pull a goal back through Matip with 12 minutes remaining but it was not enough as Jens Keller's men joined fellow top-flight clubs Mainz, Stuttgart, Augsburg and Paderborn in making first-round exits.
It was a different story for Hamburg, who progressed to the next round, albeit on penalties against Energie Cottbus at the Stadion der Freundschaft.
Hamburg emerged 4-1 winners in the shoot-out after scores were locked at 2-2 at the end of extra time.
Cottbus, who were relegated to 3.Bundesliga last season, hit the front courtesy of Manuel Zeitz's 10th-minute penalty but visiting Hamburg were back on level terms with 20 minutes remaining, when Heiko Westermann headed home the equaliser.
That forced extra time and both teams exchanged goals with Rafael van der Vaart's 96th-minute free-kick putting Hamburg ahead, only for Sven Michel to hit back nine minutes later as penalties beckoned.
Cottbus had no answer in the shoot-out, missing two of their three attempts as Hamburg converted their first four to book a spot in the second round.
In other results on Monday, Heidenheim were 2-1 winners over 2.Bundesliga rivals Union Berlin.
Fourth-tier side Kickers Offenbach stunned Ingolstadt, who play in the second division, 4-2 on penalties following their 0-0 draw at the end of 120 minutes.
|Man City pay training-pitch tribute to Joe Hart|
|Neymar to be rested as Tuchel rubbishes Ballon d´Or concerns|
|Sarri ´not interested´ in Christensen father´s quit threat|
|Cardinals fire offensive coordinator McCoy after 1-6 start|
|Neymar return unlikely, but anything can happen – Valverde|
|Bairstow a doubt for fourth ODI|
|Manchester United fined for late arrival and delayed kick-off against Valencia|
|Australia-Pakistan chat not ´especially polite´ - Sarfraz|
|Pogba relishing ´pressure game´ against in-form Hazard|
|Don´t bet on Cardiff survival, warns Warnock|
|Buffon enjoying Tuchel´s methods at PSG|
|RIP to Wimbledon epics! Isner feels like The Undertaker following final-set tie-break rule|
|Sevilla performance sealed Bernat´s Bayern exit - Hoeness|
|Keita set to miss out as Liverpool monitor injured stars|
|He didn´t want to be here – Guardiola doubts Sancho will return to Manchester City|
|Sarri: Manchester United are the best in the Premier League|
|Mourinho salutes ´brave´ Shaw for ´best possible´ response to criticism|
|No Ballon d´Or distractions for Griezmann, insists Simeone|
|Wigan stand by Hardaker as full-back prepares to undergo rehabilitation|
|Barcelona deny Neymar talk|
|Hazard can win the Ballon d´Or as a Chelsea player, insists Sarri|
|De Bruyne in contention to start in Manchester City´s clash with Burnley|
|Neymar needs to mature to reach Messi levels - Xavi|
|We have a hell of a lot to do - Paine slams Australia batting|
|Kerber and Osaka to meet at WTA Finals|
|Lorenzo out of Japanese MotoGP|
|Real Madrid handed Africa trip in Copa del Rey|
|Allegri: Ronaldo has sharpened Juventus focus|
|No Wade in Wasps squad amid NFL reports|
|Rooney: Five of us controlled Man United dressing room|
|Bayern bosses launch scathing attack on ´disrespectful´ media|
|Saints lock in Lawes to new deal|
|Adelaide United 1 Sydney 1: Debutant Le Fondre rescues a point|
|Madrid can´t look back, only forward - Lopetegui confident of revival|
|Wimbledon to introduce final-set tie-breaks|
|Abbas inspires Pakistan to series victory|
|Madrid boss Lopetegui hopeful on Bale availability|
|Mood is positive at Bayern, insists under-pressure Kovac|
|LeBron offers food for thought after losing Lakers debut|
|Bolt future not an immediate concern for Mariners|
|Hazard: I could finish my career at Chelsea|
|Buffon hoping to avoid Champions League final against Juventus|
|Wilshere not ready for West Ham return|
|Chelsea v Manchester United: Hazard better under Sarri than he ever was with Mourinho|
|The big Friday Premier League quiz|
|Khawaja suffers meniscal tear, doubt for India series|
|Babbel: Klopp must win trophies now at Liverpool|
|LeBron makes spectacular start on Lakers debut, but LA fall to Trail Blazers|
|Broncos thrash Cardinals to end losing streak|
|Price leads Red Sox past Astros and into World Series|
|LeBron makes fast start on Lakers debut with two massive dunks|
|Real Salt Lake 4 New England Revolution 1: Hosts boost play-off chances|
|Simmons gets triple-double in win over Bulls|
|´Ambitious´ Maguire wants Champions League football|
|Henry praises ´charismatic leader´ Falcao|
|WATCH: Cardinals WR Fitzgerald tackles former QB Warner on sidelines|
|Spurs right not to make signings – Pochettino|
|Icardi happy at Inter, close to contract renewal|
|This Week in U.S. Sports: Bosa leaves Ohio State while the World Series is almost set|
|Liverpool boost as Salah and Van Dijk join training|
|Cowboys discuss road woes, Prescott says team ´addressed the elephant in the room´|
|Isner scrapes through in Stockholm, Monfils eliminates Tsonga|
|Hinch says Altuve would be out with injury in regular season|
|WATCH: Schwarzenegger tells LeBron to make Lakers great again|
|LeBron tells Lakers coach Walton: I´m always fresh!|
|Mayweather should come back to fight me - Alvarez|
|Goerges battles past Vekic, Kasatkina wins all-Russian tie|
|Ask 32,000 Gibraltarians if the Nations League is meaningless - Styche|
|They´re going to speak about it for years - Azhar reflects on comical run out|
|Garcia in the mix as weather hits Andalucia Valderrama Masters|