"We delivered a top performance and deserved to win," said Poulsen.
"After a game like that, confidence is high and puts a spring in your step."
The victory keeps second-placed Leipzig two points behind leaders Bayern Munich, who earlier romped to a 5-1 home win over Cologne.
Gladbach were in complete control at half-time after Hofmann netted an early penalty and Thuram used his shoulder to guide the ball into the net from a Breel Embolo header.
However, Sorloth came off the bench and inspired the second-half fight back.
The former Crystal Palace striker had a goal disallowed for handball before setting up Nkunku, who fired home Leipzig's first goal on 57 minutes.
Poulsen smashed home the equaliser on 66 minutes.
Leipzig had all the momentum and peppered the Gladbach goal before Sorloth's winning header deep into added time.
Goretzka shines for Bayern
Earlier, Bayern bounced back after taking just a point in their previous two league games as midfielder Leon Goretzka created three goals in their rout of Cologne.
Eric Maxim Choupo-Moting headed Bayern into an early lead before Robert Lewandowski, the league's top scorer, struck twice to increase his league tally to 28 goals this season.
Serge Gnabry came off the bench to claim two late goals behind closed doors at the Allianz Arena on his first appearance since tearing a thigh muscle in Bayern's Club World Cup final win in Qatar.
Coach Hansi Flick made just one change - Choupo-Moting for Kingsley Coman - from the side which beat Lazio 4-1 in the Champions League on Tuesday.
Bayern quickly built a 2-0 lead through Choupo-Moting and Lewandowski with Goretzka setting up both goals.
However, Cologne midfielder Ellyes Skhiri chipped Manuel Neuer four minutes after the break to pull a goal back.
With just over 25 minutes left, Flick settled nerves by bringing on Gnabry and Thomas Mueller, who made his first appearance a fortnight after testing positive for Covid-19.
Mueller's pass split the Cologne defence and found Lewandowski who restored the two-goal cushion on 65 minutes.
Cologne midfielder Dominick Drexler hit the post before Gnabry made it 4-1 by converting a cross, then claimed his second just before the final whistle after an excellent pass from Goretzka.
Wolfsburg remain third, seven points behind Bayern, after their 2-0 home win over Hertha Berlin, whose defender Lukas Kluenter turned the ball into his own net before Maxence Lacroix scored the hosts' second.
Wolfsburg defender Marin Pongracic was sent off in added time for a second booking.
England winger Jadon Sancho converted a penalty and Brazil midfielder Reinier scored his first goal for the club as Dortmund stayed fifth with a 3-0 home win over Arminia Bielefeld.
Japan midfielder Wataru Endo netted his first two Bundesliga goals in Stuttgart's 5-1 thrashing of bottom side Schalke, whose Algeria midfielder Nabil Bentaleb had a second-half penalty saved.
On Friday, fourth-placed Eintracht Frankfurt had their 11-match unbeaten run ended by a shock 2-1 defeat at Werder Bremen, whose rising American star Josh Sargent, 20, hit the winning goal.