Leipzig opened the scoring through Xavi Simons 15 minutes in but Sargis Adamyan equalised almost immediately and the scores were level at the break.
But Openda then struck in the 63rd and 67th minutes before Amadou Haidara and Yussuf Poulsen padded the score for the visitors.
Leipzig move two points above Borussia Dortmund, who take on Eintracht Frankfurt on Sunday.
Borussia Dortmund head coach Niko Kovac has hinted at several changes to his line-up ahead of Friday night's Bundesliga match at FC Augsburg, following a gruelling 120-minute cup tie against Eintracht Frankfurt in midweek.
Bayern Munich's sporting chief Max Eberl has defended Luis Diaz after the Colombian forward missed another big opportunity during their 4-1 DFB-Pokal victory over FC Koln on Wednesday night.
Jonas Urbig has praised Bayern Munich's mentality and team spirit after playing a starring role in their 4-1 comeback victory over FC Koln in the DFB-Pokal second round on Wednesday.
Bayern Munich's blistering form under Vincent Kompany reached historic levels as they stormed into the DFB-Pokal round of 16 with a 4-1 victory over Koln.
