There were also wins for Nicolas Almagro and Daniel Gimeno-Traver in Bastad, Sweden, with Fernando Verdasco and Alexandr Dolgopolov going through in Umag, Croatia.
And in the United States, Lleyton Hewitt progressed to the semi-finals of ATP Newport with a 6-4 6-3 win over Dudi Sela.
Monaco was utterly commanding throughout in Stuttgart as he took the match in straight sets, and sealed his place in the last eight.
The world number 14 won 67 per cent of his service points and saved seven of eight break points to overcome Kamke, who could not match his opponent's intensity or power from the back of the court.
Monaco will next take on Pavol Cervenak after the Slovakian stunned Germany's Tommy Haas 6-4 6-4.
Australian Tomic, meanwhile, failed to recover from losing a first-set tie-break to the Brazilian Bellucci, losing 7-6(6) 6-3.
The world number 64 won saved eight of 10 break points to make the last eight at his first ATP Stuttgart.
Bellucci will face Germany's Cedric-Marcel Stebe after he came from a set down to stun Frenchman Jeremy Chardy 4-6 7-6 6-3.
The other two quarter-finals see Janko Tipsarevic face Germany's Bjorn Phau, with another German Dustin Brown in action against Spain's Guillermo Garcia-Lopez.
Nicolas Almagro suffered a scare at the Swedish Open in Bastad before overcoming Ivor Minar 1-6 7-6(8) 6-4 to reach the quarter-finals.
The second seed was convincingly beaten in the first set by Czech qualifier Minar, the world number 216.
But Spaniard Almagro, the 2010 champion, battled back to take the second-set tie-break 10-8 before breaking and holding to take the decider.
Next up for Almagro is compatriot Daniel Gimeno-Traver, who beat Italian qualifier Alessandro Giansessi 6-4 6-3.
Third seed Alberto Ramos eased past Kazakh qualifier Evgeny Korolev 6-3 6-3 to seal his place in the quarters.
The Spaniard faces Bulgarian star Grigor Dimitrov for a place in the semis.
The other two quarter-finals will be between Spain’s top seed David Ferrer and compatriot Tommy Robredo, while Estonia’s Juergen Zopp faces Jan Hajek of the Czech Republic. Those match-ups were determined on Wednesday.
In Croatia, top seed Fernando Verdasco of Spain beat Ernests Gulbis of Latvia 6-2 3-6 6-1 to move into the quarter-finals.
Verdasco faces Russia's Andrey Kuznetsov next, after he beat local hope Mate Pavic 7-6(0) 6-1.
Third seed Alexandr Dolgopolov of Ukraine beat Fabio Fognini of Italy 6-2 6-4 to set up a clash with Carlos Berlocq.
Fifth-seeded Argentine Berlocq beat compatriot Marco Trungelliti 7-6(4) 4-6 6-1.
At Newport, there was a combination of second round and quarter-final matches in play on Thursday.
In the second round, Benjamin Becker of Germany ousted highly-rated young Canadian Milos Raonic 6-3 6-3. Raonic was the third seed.
In the other last-16 clash on Thursday, American sixth seed Ryan Harrison beat compatriot Jesse Levine 6-3 6-4. Harrison will now face Becker for a place in the semis.
After those matches were completed, Hewitt came up against Israel’s Dudi Sela, the Australian winning 6-4 6-3.
He will face America's Rajeev Ram for a place in the final after he shocked Japan’s Kei Nishikori 7-6(8) 6-3.