Emil Forsberg's superb opening goal put UEFA Champions League semi-finalist Leipzig ahead, but it was cancelled out by an equally impressive long-range effort from Leverkusen's Kerem Demirbay.
Leverkusen's new signing Patrik Schick, who spent last season on loan at Leipzig, curled in a superb shot from 16 metres out but this stunning strike was ruled offside with 23 minutes left.
Elsewhere, Borussia Moenchengladbach had to settle for a point at home to Union Berlin in a 1-1 draw.
Marcus Thuram's headed goal for Gladbach on 56 minutes was cancelled out by an equaliser from Union defender Nico Schlotterbeck, 20, making his first Bundesliga appearance for the Berlin-based club, with 11 minutes left.
History was made in Arminia Bielefeld's 1-0 win at Cologne as Joan Simun Edmundsson, 29, came on to score the winner and became the first Faroe Islands footballer to play and score in the Bundesliga.
Meanwhile, newly-promoted Stuttgart romped to a thumping 4-1 win at 10-man Mainz.
Sweden forward Robin Quaison scored early on for Mainz, but Congo winger Silas Wamangituka equalised just before half-time with his second goal in as many weeks after finishing a counter-attack.
Daniel Didavi added Stuttgart's second on 61 minutes after a simple tap-in, just before Mainz was reduced to 10 men when French centre-back Moussa Niakhate was shown a red card for a second booking.
The visitors profited with goals in the final 10 minutes through replacement Mateo Klimowicz and forward Sasa Kalajdzic as Stuttgart earned a first league win at Mainz for 15 years.