Leading 3-2 at home but staring at an exit on the away goals rule, Tigres UANL needed some heroics deep in additional time.
Up for a set-piece, Guzman incredibly headed in an Eduardo Vargas free-kick to give Tigres a 4-2 victory and 5-4 aggregate win, sending them into the quarter-finals.
The 34-year-old goalkeeper was unmarked when he met Vargas' delivery in the 94th minute midweek.
Enner Valencia's opener and an Andre-Pierre Gignac brace had put Tigres in control before Juan Carlos Portillo Leal's double for Alianza.
Tigres, who have made a slow start to the Liga MX Clausura season, will face New York City in the last eight.
Bundesliga champions Bayern confirmed Muller's absence on Thursday, just hours before they were due to face the Mexican side at the Education City Stadium in Qatar.
Muller is the latest player in Bayern's squad to return a positive test for COVID-19, with Javi Martinez and Leon Goretzka both having not travelled.
The 31-year-old has isolated and, upon returning to Munich, will immediately quarantine. There were no further positive tests recorded in Bayern's squad.
Bayern are also without Jerome Boateng against Tigres after he returned to Germany following the death of his ex-girlfriend.
Robert Lewandowski scored twice as Bayern defeat Al Ahly 2-0 in Monday's semi-final to book their fixture with Tigres.
CONCACAF Champions League silverware had eluded Tigres, who were runners-up in 2016, 2017 and 2019.
But Tigres finally got their hands on the Champions League trophy thanks to Tuesday's come-from-behind 2-1 victory over LAFC.
Diego Rossi's 61st-minute opener for LAFC was cancelled out by Hugo Ayala 11 minutes later before Andre-Pierre Gignac netted the winner with six minutes remaining as Tigres secured their place at February's Club World Cup in Qatar.
LAFC were bidding to make history at Exploria Stadium in Orlando, where Bob Bradley's side were looking to become the first MLS team to win the continental tournament in its current format – LA Galaxy claimed the CONCACAF Champions' Cup in 2000.
Rossi's goal just past the hour-mark had LAFC on track to snap Mexico's stranglehold on the Champions League, after the 2020 MLS Golden Boot winner found the back of the net with a lofted finish.
Liga MX giants Tigres, however, responded in the 72nd minute when centre-back Ayala sent a ball past LAFC goalkeeper Kenneth Vermeer.
Tigres completed the comeback via former France international Gignac, who finished from outside the box to earn Golden Boot and MVP honours.
"At last! It is deserved for the institution... I always wanted to win the CONCACAF Champions League," Gignac said afterwards. "Today it's Tigres' turn.
"It's for all the people back in Monterrey working in the offices. This is for the people in Monterrey."
