The victory, on an electric Etihad Stadium evening, helped us qualify for the quarter-finals of the illustrious competition for a sixth consecutive season.
Haaland became the third player to score five goals in a single Champions League game after Luiz Adriano in October 2014 (Shakhtar Donetsk v BATE Borisov) and Lionel Messi in March 2012 (Barcelona v Bayer Leverkusen).
He has also now scored 33 goals in 25 games in the Champions League, reaching the 30-goal milestone in fewer matches than any other player in the competition’s history – and becoming the youngest player to reach 30 goals in Champions League history at 22 years and 236 days.
Haaland now has a remarkable 39 goals from 36 games - breaking Tommy Johnson's club record of 38 goals in a single season set in 1928/29.
It didn’t take long for the hosts to fashion the opening chance, Ilkay Gundogan skying over a shot in the box on three minutes following a pinpoint cross from the recalled Kevin De Bruyne on the right flank.
Nathan Ake produced a fine flighted ball into the path of an onrushing Haaland on 11 minutes but the star striker couldn’t prod it home past the alert Janis Blaswich as City began to crank up the pressure.
There was a melee inside the Leipzig box on 19 minutes but the visitors appeared to have cleared the danger after several half-chances for the hosts.
However, referee Slavko Vincic was called to the VAR monitor to assess a potential handball by Benjamin Henrichs and, after watching a replay, he pointed to the spot and booked the right-back.
Haaland stepped up to the spot on 22 minutes and made no mistake, firing home past Blaswich.
Haaland doubled his tally for the night and put us into a 3-1 lead just two minutes later as he nodded home from close-range after Kevin De Bruyne had smashed a stunning shot against the crossbar and, thankfully, back into the Norwegian’s path.
He almost had his hat-trick moments later as he smashed a shot towards the near post but it was palmed away by Blaswich.
Gundogan could well have made it three for the hosts on 39 minutes when he was played in delightfully down the right channel by the attentive, observant De Bruyne. The German, though, had his goalbound effort parried away by Blaswich.
Haaland had his hat-trick on the stroke of half-time, with the fab forward ensuring the ball crossed the line after Ruben Dias had an initial header saved by Blaswich.
City began the second half as they had finished the first - with intense attacking intent.
Gundogan got in on the goalscoring act on 49 minutes as the skipper twisted and turned on the edge of the box before firing an unstoppable shot past the despairing, diving Blaswich.
Haaland had his fourth of the night on 53 minutes when he blasted past Blaswich. His initial chance was well saved after the ball had been headed to him by Bernardo Silva. It then fell to Manuel Akanji who also was denied but Haaland didn't let a second opportunity allude him as he fired home.
Number five was not far behind for the towering forward as he finished expertly once again on 57 minutes.
There were a flurry of substitutions for both sides just before and just after the hour mark with the game all but settled.
They did affect the flow of the game but then nothing could compare to the scintillating start to the second period.
City did keep pushing and prodding for more and the night ended on another high note as De Bruyne fired home an unstoppable shot in stoppage time.
LEIPZIG XI: Blaswich, Henrichs (Klostermann 80'), Orban (c), Gvardiol, Raum, Haidara (Simakan 63'), Laimer, Forsberg (Andre Silva 63'), Szoboszlai (Olmo 72') Kampl, Werner (Poulsen 63')
Unused subs: Nyland, Nickisch, Halstenberg, Ba
PLAYER OF THE MATCH: ERLING HAALAND
One word for his display against RB Leipzig - unplayable!
ON TO THE QUARTERS
We're now one of six teams to progress through to the Champions League quarter-finals so far.
We follow Chelsea, Bayern Munich, AC Milan, Benfica and Inter Milan into the last four of the competition.
Tomorrow, another two teams will progress to finalise the names in Friday’s draw.
Napoli host Eintracht Frankfurt as they look to build on their 2-0 first leg lead while Real Madrid welcome Liverpool to the Bernabeu Stadium, with what looks like an unassailable 5-2 advantage from the opening game at Anfield.
City have now won each of our last 10 UEFA Champions League matches against German clubs as the home side.
That sequence was confirmed with tonight’s 7-0 victory over RB Leipzig as we progressed through to the last eight of the competition for the sixth consecutive season.
We have also scored at least two goals in each of those matches.
Ironically, the last German club to win away at City in this competition were a Pep Guardiola-led Bayern München side in 2013/14.
On Erling Haaland: "Five goals. Fabulous.
"What can I say? I said many times, he’s a joyful guy. He is a gift to all of us.
"His mood in the locker room is always happiness.
"He is a huge competitor, his mentality is there.
"He scored five goals which is not easy."
"It’s a big night.
"First of all to play in the Champions League, I’m proud to play in it - I love this competition as everyone knows.
"Five goals and to win 7-0 at home, I’m so happy.
"A lot of goals today I did not think, I was just doing it. Same with every goal, I didn’t think.
"A lot of it is being quick in the mind and putting it where the keeper is not."
WHAT IT MEANS
We’re through to the quarter-finals of the Champions League.
We will find out who we will face in the last eight when the draw is made this Friday, with an 11:00 (UK time) start in Nyon, Switzerland.
It’s our sixth consecutive season reaching this stage of the competition.
In previous years, we have faced Atletico Madrid (2021/22), Borussia Dortmund (2020/21), Lyon (2019/20), Tottenham (2018/19) and Liverpool (2017/18).
Let’s see who we get this time around!
We compete in our third competition in as many games when we host Burnley in the FA Cup this weekend.
That follows a clash with Crystal Palace in the Premier League on Saturday and RB Leipzig tonight in the Champions League.
The game with the Clarets, managed of course by City hero Vincent Kompany, takes place on Saturday 18 March, kick-off 17:45 (UK time).