كتب : Hatem Maher
The Werder Bremen striker netted twice in the first half before Lucas Podolski completed the rout in the second period.
The result means Germany finish their Group A as winners with a perfect nine points while Ecuador advance to the round of 16 as runners up.
The hosts will now take on Group B runners up, who will be determined later on Tuesday while Ecuador face the group winners.
Klose broke the deadlock as early as the fourth minute after he met Bastian Schweinsteiger's back pass inside the area with a first-timer into the back of the net.
Two minutes before the break Michael Ballack chipped the ball over the defense to Klose who rounded the keeper and slotted the ball into the empty net to extend Germany's lead.
In the 57th minute, Podolski opened his scoring account in the World Cup when he connected with Bernd Schneider's neat cross before poking the ball into the bottom left corner.
In the other Group A match, Bartosz Bosacki scored two goals as Poland came from behind to beat Costa Rica 2-1.
Costa Rica took the lead through Ronald Gomez in the 25th minute before two strikes from Bosacki in the 33rd and 66th minutes sealed the victory for the Poles.
The win gave Poland their first three points of the tournament to finish third and bid Germany farewell along with Costa Rica who failed to grab a single point.