Bayern reached the last 16 of the competition thanks to a 5-4 win on penalties after Wednesday's clash finished 1-1 following extra time at Red Bull Arena.
There was plenty of drama during the 120 minutes as referee Felix Zwayer changed his mind in awarding Leipzig a first-half penalty before pointing to the spot in the second period – which Emil Forsberg converted – and sent off Naby Keita for two yellow cards.
Thiago Alcantara equalised to force extra time but penalties were needed and Bayern goalkeeper Sven Ulreich – filling in for injured number one Manuel Neuer – proved to be the hero after denying Timo Werner.
"Penalties are always a lottery, but my players were very focused and converted very well," Heynckes said.
"It's an extremely important win to us."
Ulreich got down low to save Werner's weak penalty after nine successful spot-kicks and the Bayern shot-stopper said: "It is always nerve-wracking when it goes to penalties, but I'm just happy to have helped the team reach the next round.
"I want to pay a big compliment to our goalkeeping coach [Toni Tapalovic] who is always great at analysing these things.
"I only managed to save one but it proved decisive as the lads converted all their penalties well."
Bayern captain Arjen Robben, whose side will face Leipzig again in the Bundesliga on Saturday, added: "It was football at a high level with two top teams playing. There is too much to analyse. It was a fiercely intensive game with a red card. We conceded the penalty against their 10 men but luckily, we got the equaliser. Then, of course, we created many chances and were unlucky not to score again.
"Heynckes had told us to prepare for the game like a final. Perhaps we were lacking a little freshness as we play every three days, so playing 120 minutes is not very pleasant. Thankfully, we are playing against each other again on Saturday so they have the same problem. But we are very happy to progress to the next round."