Louis van Gaal's side moved on to 18 points, seven clear at the top of Group D, after second-placed Hungary drew 1-1 with Turkey.
"This was the best match under my management so far," Van Gaal said.
"We executed our game plan much better than we did on Friday (in a 3-0 win over Estonia). We only played sloppily in the final quarter of the first half and that resulted in their sole chance of the match."
World champions Spain who scored a hugely significant 1-0 win over France in Paris.
Germany also moved a step closer to the finals when they followed up Friday's 3-0 win in Kazakhstan with a 4-1 victory over the same opposition in Nuremburg to climb to 16 points and open up an eight-point gap at the top of Group C.
Sweden, who did not play, Austria and Ireland are all on eight points after the latter drew 2-2 with the Austrians in Dublin after the visitors salvaged a point with an equaliser from David Alaba in the 92nd minute.
Reus added a fourth in stoppage time to give Germany their fifth win in six qualifiers as they also hit the woodwork six times in a one-sided game that at times looked like a friendly.
"Obviously, in the second half our concentration and our presence was not as strong but we still could have scored two or three more goals. But the game was decided by then," Germany coach Joachim Loew said.
"Kazakhstan had 10 men around the box and waited for us but did little else. They did not want to play football."
Italy also consolidated top spot in their section when they won 2-0 in Malta with a double from in-form Mario Balotelli to move three points clear of second-placed Bulgaria who drew 1-1 in Denmark in their Group B game. Italy now have 13 points.
Balotelli, buoyed by his outstanding goal in a 2-2 friendly draw with Brazil on Thursday, again delivered for Italy who survived two first-half scares before applying the killer blow with a second goal in the dying minutes of the opening half.
"We have to treasure the fact that when we come up against a well-organised team we have to be quicker with our play," Italy coach Cesare Prandelli told Rai television.
"But the great performance against Brazil and the three points tonight are paramount."
Balotelli opened the scoring with a sixth-minute penalty after Malta defender Luke Dimech floored Stephan El Shaarawy in the penalty area but Malta refused to lie down.
Their bold reaction unsettled Prandelli's men whose struggles were laid bare when, after 16 minutes, goalkeeper Gianluigi Buffon brought down Malta midfielder Andre Schembri in the box after an intelligent pass from Roderick Briffa.
Michael Mifsud marched towards the spot but his low effort was stopped by Buffon.
A Jekyll and Hyde display from England left their World Cup qualifying hopes in jeopardy as Montenegro's spirited fightback earned the tiny Balkan nation a 1-1 draw which kept them in control of Group H.
Belgium and Croatia, who started the day joint-top of Group A with 13 points, stayed neck-and-neck after Belgium beat visitors Macedonia 1-0 with a goal from Eden Hazard and Croatia won 2-1 in Wales with late goals from Dejan Lovren and Eduardo.
The pair are nine points clear of third-placed Serbia, who won 2-0 against Scotland who became the first team in the European qualifiers to be mathematically eliminated as they cannot catch either of the joint leaders Belgium or Croatia.
Portugal rekindled their chances by winning 2-0 in Azerbaijan after stumbling to a 3-3 draw against Israel on Friday to move within a point of Group F leaders Russia, who did not play.
The Israelis also maintained their hopes of a first World Cup finals appearance since 1970 with a 2-0 win over Northern Ireland in Belfast to stay level with Portugal on 11 points.