Gabriel Landeskog scored the game's only goal 5:26 into the second period as Colorado improved to 8-1, the best start in franchise history.
The game was billed as a fight for bragging rights between Pittsburgh star Sidney Crosby and Colorado rookie Nathan MacKinnon. The former No. 1 picks both are from Cole Harbour, Nova Scotia in Canada.
Instead, Giguere stole the show. Pittsburgh went 0 for 7 on the power play and lost for the first time at home despite outshooting the Avalanche 34-14.
Marc-Andre Fleury stopped 13 shots for the Penguins (7-2).
The first professional meeting between MacKinnon and Crosby failed to produce fireworks, not that Crosby didn't try. He pumped a season-high seven shots at Giguere and played more than 26 minutes.
MacKinnon, by comparison, produced two shots in 10:54 of ice time as the Avalanche spent a large portion of the night relying on their penalty killers to hold off one of the NHL's most potent offenses.
Still, MacKinnon and Crosby figure to spend most of the next decade talking about each other.
MacKinnon spent most of his childhood growing up in Crosby's considerable shadow in the town of about 25,000 hard against the Atlantic Ocean. He followed a similar path to the NHL, playing on the same junior team as Crosby and showcasing prodigious talent as a playmaker.
Taken with the league's top overall pick nearly a decade after Crosby, MacKinnon has a goal and six assists through his first nine games, a pace not too far off the one Crosby set during his rookie year in 2005-06.
Crosby said before the game he's hardly surprised at how well MacKinnon has fit in but the two brushed aside any talk of a battle for local bragging rights, perhaps because their arrivals into the NHL couldn't be more different.
Unlike Crosby, whose presence almost single-handedly revitalized a sagging franchise, the 18-year-old MacKinnon is not viewed as a savior, but a piece of what is quickly becoming a compelling puzzle.
The Avalanche have been nothing short of a revelation during the season's opening weeks thanks to steady goaltending and the first-year head coach Patrick Roy's fiery competitiveness.
They needed both to withstand three periods of steady pressure from Crosby.
The Penguins dominated the early going, but had nothing to show for it as four power plays went to waste.
Buzzing Giguere constantly, Pittsburgh peppered the veteran from all angles. The 11-4 advantage in shots didn't even include the dozen Giguere's teammates blocked before they even made their way to the net.
Colorado steadied itself in the second period and caught a bit of a break when the puck made its way to Landeskog shortly after he exited the box after serving a hooking penalty.
He skated into the Pittsburgh zone and fired a wrist shot from the right circle that handcuffed Fleury and sailed into the net for his third goal of the season.
It was enough to send the Penguins into the dressing room trailing at home after two periods for the first time this season.
The Avalanche felt comfortable enough with the lead to sit back and frustrate the Penguins.
Colorado didn't even take a shot for the first 12 minutes of the third period, more intent on keeping the puck out of their net instead of sending it behind Fleury.
It worked. Giguere was spectacular at times, no more so than when he robbed Chris Kunitz with a glove save at the end of a 2-on-1 break with less than 8 minutes remaining.
Pittsburgh D Kris Letang skated with his teammates on Monday morning, but remains out with an undisclosed lower body injury. Coach Dan Byslma said the Norris Trophy finalist is nearing a return ... The Avalanche scratched D Nick Holden, D Tyson Barrie and F Cody McLeod ... The Penguins are off until Friday, when they host the New York Islanders. The Avalanche head home to play Carolina on Friday.