Both sides struggled to impose themselves in the first half before Ederson broke the deadlock in the 62nd minute with a low strike past Maribor keeper Jasmin Handanovic.
Maribor were then reduced to 10 men when Jovan Vidovic was dismissed for a foul on Sergio Floccari in the area, with Anderson Hernanes unable to double Lazio's lead from the resulting penalty thanks to a fantastic save by Handanovic.
Last time the Slovenian champions faced the Italian giants in European competition was 13 years ago when they were beaten 4-0 home and away.
The performance, while not another win to add to their 3-0 victory over Panathinaikos in their Group J opener, still showed a vast improvement from the heavy defeats in 1999.
Maribor had the first chance of the match in the 13th minute when midfielder Zeljko Filipovic struck the bar with a close range header.
Lazio defender Andre Dias fired a chance over the bar minutes later before Antonio Candreva hit the post as both sides struggled to find the opener.
Candreva then fired over the bar before Lazio midfielder Hernanes did the same as the Italians struggled to convert their home advantage.
There were few other clear cut chances in the first half, with the next chance coming after the break when Ederson's wayward shot missed the Maribor keeper's left post.
The Lazio midfielder finally found an opening just after the hour mark when he pounced on a loose ball parried by Handanovic to send in a low strike from the middle of the area.
Vidovic was then shown red, but despite Hernanes missing from the spot, Lazio held on for a win and moved top of Group J.