Sami Khedira’s deflected shot gave the hosts a 12th-minute lead and Andre Schuerrle made it 2-0 in the second half following a fine turn.
Mesut Ozil then made sure of victory with the third goal in stoppage time.
Despite having more than half a dozen injury absentees, Germany were always in control with midfielder Bastian Schweinsteiger back in the side after a six-month break to earn his 99th cap.
Germany have 25 points from nine games and an unassailable lead at the top of the group before they face second-placed Sweden in Stockholm on Tuesday.
Arsenal midfielder Ozil was played up front due to injuries to Mario Gomez and Miroslav Klose as the hosts fielded six Bayern Munich players in their line-up.
Ireland, with interim coach Noel King in charge after the departure of Giovanni Trapattoni last month, went close through Kevin Doyle in the opening minutes before Germany stepped up a gear.
Khedira struck when his shot from the edge of the box went in off Ireland defender Ciaran Clark.
Keeper David Forde denied Germany a second goal in the 35th minute, spectacularly fisting a thunderous Schuerrle header away.
At the other end Clark almost made amends for his earlier mistake when his header hit the bar on the stroke of halftime.
Germany made it 2-0 in the 58th minute when Schuerrle controlled a fine Toni Kroos chip in the box before blasting the ball beyond Forde.
The Irish forced keeper Manuel Neuer to make a double save in the 73rd minute and Jerome Boateng responded for Germany with an unstoppable shot that rattled Forde’s crossbar.
(Reporting by Karolos Grohmann; editing by Tony Jimenez)