Daizen Maeda was sent off after a booking was reassessed via the monitor, with the visitors trailing to Griezmann’s early deflected strike.
Morata added a close-range finish before the interval and thundered in the fifth after great efforts from Griezmann and Samuel Lino, while Saul scuffed in the sixth.
With two games remaining, Brendan Rodgers’ side are five points adrift of Feyenoord in third place.
Atletico lead the way on eight points, one ahead of Lazio, who Celtic visit next.
Celtic’s solitary point came against the Spanish side in Glasgow a fortnight ago. That was a thrilling contest with no quarter given. This was a mundane, one-sided affair by comparison, given the visitors’ miserable start, although there was much to admire in the hosts’ ruthlessness and fine finishing.
The game completely raced away from Celtic as Diego Simeone’s team seized on their personnel advantage, which came after referee Ivan Kruzliak was asked to review the yellow card he had given Maeda for catching Mario Hermoso on the shin.
The harsh red card played a massive part, but the nature of the opening goal will also frustrate Rodgers, given Celtic had started brightly.
It felt both key and avoidable as Callum McGregor nodded into a dangerous area outside the box. That was compounded by it landing at the feet of Griezmann, who sent in a shot that cruelly diverted beyond Joe Hart.
Celtic’s response was initially strong. They held onto the ball well and Maeda, in particular, caused problems down the right. That threat came to an abrupt end when he went into a challenge with a raised boot, Hermoso went down and the Atletico players, on the pitch and on the sidelines, reacted with animated fury.
Rodgers was incensed by counterpart Simone’s role in the protests as the yellow card was upgraded to red.
Morata’s strike just before half-time ended Celtic hopes as he slid in to meet Jose-Maria Gimenez’s nod across goal.
The Spanish side were utterly merciless from that moment, oozing quality and scoring some exceptional goals.
Griezmann’s second, an overhead kick, was brilliant giving Hart little chance.
Substitute Lino more than matched that when he bent a lovely shot into the far corner.
The trend continued when Morata crashed in a swerving fifth from the edge of the penalty area and a late sixth arrived when Saul poked home.
In truth, it could have been more with both Angel Correa and Gimenez denied by the woodwork in a torrid second half for Celtic.
Player of the match – Antoine Griezmann
Top class Atletico punish red card – analysis
With 11 players, Celtic might have suffered against this side. With 10 it was impossible. It all fell apart after a promising opening. Maeda’s dismissal, Celtic’s third in this campaign, was a hammer blow against opposition who showed incredible hunger to chase goal after goal.
Rodgers was upset by the decision but will also be unhappy with some of the defending at crucial moments. That said, some of Atletico’s goals were truly exceptional. Their work-rate, tactics and execution were top class as Celtic’s night went from bad to worse.
A painful setback after signs of improvements at this level.
What they said
Celtic manager Brendan Rodgers: “It’s a huge gulf, you see that. These players gave everything. The sheer quality of Atletico overrides our effort.
“I feel for the players. We were undeserving of the red card, and when we get it, it’s a huge challenge.
“When you see the images that the referee has seen, it wasn’t representative of the actual challenge.
“I don’t want to go on about the officials. You have to accept decisions. It feels more like a computer game, the constant looking at the screens.”
Atletico Madrid forward Antoine Griezmann: “We started the match really well and not doing that is something that has cost us before. Then the sending off gave us calmness, more space to play in. The team has played a really good game, we need to continue like this.”
- Atletico Madrid recorded their biggest ever margin of victory in Champions League match, scoring six goals in a single game in the competition for the first time.
- Celtic remain winless in 14 Champions League games (D3 L11), while tonight was their biggest defeat in the competition since November 2017 (7-1 against PSG).
- Atletico Madrid have won a Champions League group stage game without conceding for the first time in 16 such games, since a 2-0 away win against FC Redbull Salzburg in December 2020.
- Antoine Griezmann has scored in three consecutive Champions League games for the first time, having scored just once in his previous 11 matches in the competition.
- Celtic have been shown three red cards in the Champions League this season, no other team has received more than one. Indeed, the Scottish club have seen more reds in 2023-24 than across their previous 11 seasons in the competition combined (2).
- Two Atletico Madrid players (Álvaro Morata and Antoine Griezmann) have each scored two goals in a single Champions League match for the first time since September 1996 – with braces from Juan Esnáider and current Atléti manager Diego Simeone against FCSB.