Fellow substitute Isco thought his own late goal would prove decisive for Madrid but Pazzini struck in the 89th minute to earn the relegation-threatened hosts a crucial point against the LaLiga champions.
The visitors headed to Ciutat de Valencia with back-to-back league victories under their belt, prompting hopes Zinedine Zidane's men were turning the corner despite the shock Copa del Rey quarter-final loss to Leganes.
But although the Frenchman was able to name what many consider his strongest starting line-up for the first time this season, his side were twice pegged back by Levante and denied the chance to move above Valencia into third position.
Sergio Ramos headed in an early opener from Toni Kroos' corner, setting a new record as the Spain international became the first defender to score in 14 successive LaLiga seasons.
But Levante levelled before the break as a simple ball down the middle sent Jose Luis Morales racing away from Ramos and, although Keylor Navas made the save, Emmanuel Boateng was in the right place to tuck in the rebound.
Isco's goal from Karim Benzema's pass with nine minutes left appeared to have rescued Madrid, but Zidane's men fatally switched off at the back, Pazzini beating Navas with an effort that was too powerful for the goalkeeper to keep out.
Marcelo wasted two early sights of goal for the visitors, who had recorded big victories over Deportivo La Coruna and Valencia in their last two league matches, but the opener came in the 11th minute as Ramos reached 50 LaLiga goals for Madrid.
Kroos hung up a right-wing corner and Ramos - back from a calf injury - beat Oier Olazabal with a header, the goalkeeper perhaps distracted by Benzema's attempt to deflect the ball in and claim the goal for himself.
Oier recovered to block Cristiano Ronaldo's effort after badly spilling Kroos' 25-yard curler, Ivi then clearing the crossbar with a hopeful strike at the other end.
Levante had struggled to create any clear openings of their own but the hosts equalised out of nowhere three minutes before the break.
Morales burst away from Ramos but could only toe his effort straight at Navas, Boateng mopping up the loose ball to slot into the unguarded net.
Ronaldo had scored on his last four visits to Levante but Cheick Doukoure made a terrific block to deny the Portugal international, Jefferson Lerma then forcing a good save from Navas as Levante broke at pace.
Luka Modric fed Ronaldo after 63 minutes but his 20-yard shot was easy for Oier after it lost pace following a deflection, prompting Zidane to turn to Isco as a replacement for the ineffective Gareth Bale.
Oier made a brilliant one-handed save down to his left to deny Ramos, but just as a 1-1 draw looked likely, Isco came up with what seemed destined to be the winning goal.
Benzema's persistence created the chance and, when the striker worked the ball to Isco, he slammed home via a deflection off Coke.
Madrid should have shut the game down but a lack of concentration was costly as Levante scored their second equaliser with only a minute remaining.
Pazzini had only been on the pitch for 12 minutes but he got away from a poor offside trap to mark his debut in style, beating Navas from close range to earn Levante their second draw of the season against Madrid following a 1-1 at Santiago Bernabeu earlier in the campaign.