Reus and Kroos were joined on the scoresheet by Mesut Ozil and Miroslav Klose as the Germans heaped more woe on beleaguered Irish boss Giovanni Trapattoni, for whom Andy Keogh hit an injury-time consolation.
Sweden moved clear in second place in the group after coming from behind to win 2-1 in the Faroe Islands with a 75th-minute winner from Zlatan Ibrahimovic, while Austria were surprisingly held to a goalless draw in Kazakhstan.
Goals from Christian Benteke, Kevin de Bruyne and Kevin Mirallas gave Belgium a superb 3-0 win over Group A rivals Serbia in Belgrade.
Croatia stay level with the Belgians at the top of the group but only after coming from behind to win 2-1 in Macedonia. Agim Ibraimi put the hosts ahead early, before Vedran Corluka and Ivan Ratikic responded.
Two late goals from Gareth Bale gave Wales their first points with a 2-1 win over Scotland. James Morrison put the Scots ahead in the 27th minute but Bale equalised with an 81st-minute penalty and hit the winner two minutes from time.
Italy shrugged off a minor scare to win 3-1 in Armenia, Andrea Pirlo, Daniele De Rossi and Pablo Osvaldo on target for the Italians, while Henrikh Mkhitaryan briefly equalised for the hosts in the first half.
Theodor Gebre Selassie, Toma Pekhart and Jan Rezek gave the Czech Republic a 3-1 win over Malta, while Bulgaria and Denmark settled for a 1-1 draw after Nicklas Bendtner equalised Dimitar Rangelov's early opener for the hosts.
Holland cantered to a 3-0 win over Group D minnows Andorra in Rotterdam with goals from Rafael van der Vaart, Klaas-Jan Huntelaar and Ruben Schaken.
Romania maintained their 100% start in the group thanks to Grozav Grozav's goal in a 1-0 win in Turkey, while Tamas Hajnal struck the only goal as Hungary won 1-0 in Estonia.
Switzerland are still top and unbeaten in Group E despite being pegged back 1-1 against Norway. Mario Gavranovic looked to have won it for the Swiss with a 79th minute opener but Brede Hangeland equalised two minutes later.
Tim Matavs scored twice as Slovenia beat Cyprus 2-1, while Iceland won 2-1 in Albania thanks to a winner nine minutes from time from Tottenham striker Gylfi Sigurdsson.
In Group F, Alexander Kerzhakov's sixth-minute goal was enough to earn Russia a 1-0 win over Portugal in Moscow. Tomer Hemed completed a hat-trick in the final minute as Israel won 6-0 in Luxembourg.
Group G pace-setters Greece and Bosnia remain unbeaten after a tight goalless draw in Piraeus, a result that allows Slovakia to join them on seven points after Marek Hamsik and Marek Sapara scored in a 2-1 win over Latvia.
Also in Group G, two goals from Edgaras Cesnauskis were enough for Lithuania to claim a 2-0 victory in Liechtenstein.
Wayne Rooney became England's fifth highest goalscorer after scoring two in a 5-0 Group H rout of San Marino. Danny Welbeck also scored two with Alex Oxlade-Chamberlain adding the fifth on 77 minutes.
Meanwhile England's Group G rivals Ukraine were frustrated by a goalless draw in Moldova.
A hat-trick from Pedro paved the way for Spain to ease to a 4-0 win over Belarus in Minsk after Jordi Alba's 12th minute opener, while Kasper Hamalainen's equaliser gave Finland a 1-1 draw with Georgia, who had led through Guram Kashia.