All three goals in Friday's clash came from outside the box in a display that put Leipzig's recent bad away run to bed and lifted them into fourth place, equal on points with the team immediately above, Eintracht Frankfurt.
Leipzig's last away win was on December 7 - a run of seven matches without victory.
Lois Openda got the scoring started after 11 minutes. Wolfsburg lost possession in front of their own penalty box allowing the Belgian to rifle a low shot inside the far post.
A defensive mishap led to a similar second 15 minutes later. Leipzig took possession after a defender slipped and Simons made space for himself on the edge of the box, his low shot beating the goalkeeper in the exact same place.
The third in the second half was the pick of the bunch. Ridle Baku teed up Simons nicely and the Dutch international side-footed in a sublime curler from 25 metres out.
Kilian Fischer pulled a goal back for Wolfsburg and Andreas Skov Olsen brought the home side right back into the game with 16 minutes left.
But Wolfsburg could not find an equaliser and remained 12th.
In Udine, Italy, two goals before half-time put visiting AC Milan on their way to a comfortable 4-0 win over Udinese in Serie A.
The win left Milan in ninth, one point behind Fiorentina, but they will be concerned about the injury to goalkeeper Mike Maignan, who was taken off on a stretcher after colliding with teammate Alex Jiménez.
Rafael Leao's superb strike from 18 metres was quickly followed by Strahinja Pavlovic's glancing header from a corner on the stroke of half-time.
Theo Hernández added a third in the 74th minute when he started a sweeping move in his own half and finished it off with an unstoppable shot.
Substitute Tammy Abraham's superb cross led to a fourth from Tijjani Reijnders 10 minutes from time.
In Spain, Valencia beat Sevilla 1-0 to extend their unbeaten run to six games and jump to 12th place.
The win came courtesy of a Javier Guerra strike in first-half stoppage time and followed the 2-1 win against Real Madrid at Santiago Bernabeu Stadium last week.
However, the result in front of 46,000 fans at Mestalla Stadium was a bitter one for Sevilla, who in the first half had a goal disallowed and a penalty award rescinded after a video review.
The result lifted Valencia one point above Sevilla, who have lost four games in a row.
In France, a Keito Nakamura brace saw Reims boost their Ligue 1 survival bid with a 2-0 win over Lens.
The Japanese international scored in the 33rd and 88th minute to lift his side two points clear of the relegation play-off place.
In England, Burnley went back to the top of the Championship after holding on to beat Norwich 2-1 at Turf Moor and extend their unbeaten league run to 29 matches.
Goals from ex-Manchester United player Hannibal Mejbri and Jaidon Anthony before the break were reward for a dominant first-half display by the Clarets, who moved three points clear of overnight leaders Leeds.
Norwich were much improved in the second half and substitute Jack Stacey pulled one back, but Scott Parker's side stood firm to also extend their unbeaten home league run this season to 21 matches.
Leeds can go top again when they meet Preston in the early match on Saturday, with fellow promotion-chasing rivals Sheffield United meeting Plymouth Argyle at the same time.
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