Poulsen made amends for conceding a first-half penalty that was awarded after the referee consulted the VAR system, but which Peru midfielder Christian Cueva blasted over the crossbar.
With France having beaten Australia 2-1 in Kazan earlier in Group C, RB Leipzig's Poulsen showed great finishing to hit the winner on 59 minutes to the dismay of the overwhelmingly Peruvian crowd in the 40,502-capacity stadium.
The win extends Denmark's unbeaten run to 16 games without defeat and end Peru's 15-match unbeaten streak.
Peru veteran Paolo Guerrero, who only made it to the tournamenbt after late reprieve for a drug ban, came on for the final 30 minutes but his efforts at the Mordovia Arena came to no avail.
Authorities in Lima estimate around 25,000 fans flew to Russia to see their team's return to the World Cup and Saransk was a sea of Peru shirts.
Their chants were near-deafening on occasion, as were the whistles each time Denmark had the ball or dared to attack.
As a result, Peru dominated the opening 25 minutes.
Edison Flores, Andre Carrillo and Yoshimar Yotun all kept Denmark keeper Kasper Schmeichel busy.
After weathering the early storm, the Danes started to push forward.
Midfielder Thomas Delaney had their first chance when his long-range effort went over on 27 minutes.
Denmark had to bring on Ajax's Lasse Schone with 36 minutes gone when central midfielder William Kvist was stretchered off.
A yellow card was shown to Peru midfielder Renato Tapia for sending Pione Sisto tumbling just outside the area, but Christian Eriksen drilled the free-kick off the wall.
When Poulsen clipped Cueva's boot on 45 minutes, referee Bakary Gassama checked with the Video Assistant Referee and pointed to the spot for the second penalty awarded through the system of the day after France had also benefited against Australia.
Cueva took the spot-kick himself but his effort ballooned over the bar.
Just moments after Peru wasted a clear chance, when Cueva squared to Andre Carrillo who failed to connect, Denmark scored.
The ball was quickly moved forward and when Poulsen went one-on-one with Gallese, the darting Dane hit the net on 59 minutes.
Guerrero was in the thick of Peru's bid to get level and his header fell into Schmeichel's arms five minutes later.
Tottenham midfielder Christian Eriksen, who netted 11 goals in qualifying for Denmark, had to busy himself in defence to snuff out Guerrero-inspired attacks.
With just over ten minutes left, Guerrero again went agonisingly close when he pushed his shot past the post as Denmark held on.
59- Goal! Peru 0, Denmark 1.
45- Peru misses a penalty! Bad penalty by Christian Cueva !
Peru returns to the World Cup after a 36-year wait, and Los Incas will start their World Cup campaign against a talented Danish side who will be looking to progress from group C. You can watch a stream of the match from the Mordovia Arena Live & Exclusive on beIN SPORTS CONNECT.
Ricardo Gareca’s side has been handed a major boost heading into the tournament with striker Paolo Guerrero having his drug suspension lifted, allowing the 34-year old Flamengo player to take part in the tournament. Peru is coming into their match on good form, following friendly victories over Iceland, Scotland and Saudi Arabia.
Jefferson Farfan is likely to start on the left wing, and the veteran attacker played a significant role in getting Peru to the World Cup, scoring a goal in the continental play-off against New Zealand. Farfan, 33 is no stranger in playing in Russia and is currently playing for Lokomotiv Moscow.
Peru Predicted Team
Gallese; Advincula, Ramos, Rodriguez, Trauco; Tapia, Yotun; Carrillo, Farfan, Cueva; Guerrero
How to watch Online- beIN SPORTS CONNECT
TV Channel- MAX HD3
Stadium- Mordovia Stadium, Saransk
As for Denmark, they qualified for Russia after defeating Ireland 5-1 over two legs. Tottenham playmaker Christian Eriksen inspired his nation grabbing a hat-trick in the game. Much of the expectation will now fall on the 26-year-old who is set for a deep-lying playmaker role for his country.
It’s safe to say that the Danes have had uninspiring preparation period ahead of the World Cup with two 0-0 draws against Chile and neighbours Sweden. One player who just missed out on the squad is former Arsenal striker Nicklas Bendtner who was dropped from the squad after failing to recover from a groin injury. His presence in attack is a big loss for the team.
Denmark Predicted Team
Schmeichel; Dalsgaard, Christensen, Kjaer, Larsen; Kvist, Delaney; Poulsen, Eriksen, Sisto; Jorgensen
Keeper Kasper Schmeichel has been ever-present in goal for his country throughout qualification and is likely to make his World Cup debut against Peru. The Leicester City keeper enjoyed yet another solid season and could be called upon to make some crucial saves especially against a rejuvenated Peru side who will be welcoming back Paolo Guerrero into their squad.
It promises to be an interesting match as Peru who returns to the World Cup after a 36-year wait take on Denmark in their opening game of B. You can watch all the action Live & Exclusive on MAX HD3 & beIN SPORTS CONNECT.