Leipzig's poor form, in particular a 5-2 loss to Stuttgart last week, had sparked speculation about Marco Rose's future as coach of a team stacked with promising young players.
To his relief, two of those young players stepped up with the goals in a game played in driving rain on Sunday (Monday AEDT).
Openda opened the scoring from a tight angle in the 11th minute before Sesko doubled Leipzig's lead with a header just after the break.
Slovenian Sesko celebrated scoring another header off Dani Olmo's flashy "rabona" trick cross but was judged narrowly offside on video review.
Union created few chances and seemed to give up on a comeback after captain Christopher Trimmel was sent off in the 73rd for a sliding tackle into Leipzig left back David Raum's ankle.
The win over Union could steady the ship ahead of Leipzig's Champions League last-16 game against Real Madrid on February 13.
Leipzig stay fifth, with Union 15th in the 18-team league.
Earlier on Sunday, Lovro Majer had come off the bench to twice equalise for Wolfsburg in a 2-2 draw with Hoffenheim.
Maximilian Beier gave Hoffenheim the lead in the sixth minute when he received the ball wide on the left on the counter, beat defender Sebastiaan Bornauw and scored between goalkeeper Koen Casteels' legs.
Croatia midfielder Majer combined with new signing Kevin Behrens to score in the 58th, three minutes after coming on.
After Grischa Prömel's deflected shot restored Hoffenheim's lead, Majer then won a penalty and converted it to equalise once more.
Both of Sunday's games were interrupted by fans throwing objects onto the field to protest at the German league's plans to sell a slice of its marketing revenue to an outside investor.
13°C