The Germany international finished off a sweeping Leipzig move on the stroke of half-time, meaning Ralph Hasenhuttl's men will take a slender lead to the Stade Velodrome in a week's time.
Marseille will approach the second leg with optimism, however, after an enterprising display that was spoiled only by some wayward finishing.
Lucas Ocampos was particularly profligate, marring a fine individual performance, although Leipzig goalkeeper Peter Gulacsi deserved credit for a string of saves that preserved a clean sheet.
The home side enjoyed the lion's share of possession in a first half initially short on goalmouth incident, yet Marseille created the better of the opportunities.
Gulacsi had to make a fine save after nine minutes to keep out Kostas Mitroglou's clever, flicked volley from Dimitri Payet's right-wing cross.
The impressive Naby Keita had a shot blocked by the Marseille defence at the other end with Ibrahima Konate nodding Emil Forsberg's teasing cross over the bar shortly afterwards.
Ocampos was posing plenty of problems down the Marseille left and his 41st-minute cross was only partially cleared, allowing Bouna Sarr to fire a volley into the turf and on to the bar.
The opening period really came to life in the closing seconds.
Leipzig forward Jean-Kevin Augustin was denied a penalty after going down easily when his better option was to shoot just six yards out with Marseille pouring forward on the counter.
Gulacsi denied Sarr and Ocampos in quick succession with the ball eventually falling to Forsberg, who immediately launched a rapid attack.
The Swede played in Werner who cut inside on to his left foot before drilling a shot low under Yohann Pele.
Marseille continued to threaten after the break and missed three excellent chances to level within 10 minutes of the restart.
Konate denied Ocampos after the Argentine found space inside the area before the former Monaco winger wasted an even better opportunity from the resulting corner, shooting inches wide after latching on to Andre-Frank Zambo Anguissa's clever backheel.
Marseille captain Payet then shot over the bar after finding space on the edge of the area.
With Leipzig seemingly content to sit on their lead, the visitors struggled to carve out any more clear-cut chances in the final half-hour but they will be confident of overturning this deficit on home soil.