But the Frenchman popped up at the far post to turn home Nelson's cross from the right with the last kick of the game.
Hudson-Odoi maintained his impressive pre-season form throughout the first half, slotting Morata through on goal less than 10 minutes after the penalty miss, with the Spaniard once again being denied by Cech down low.
But his efforts, unfortunately, were not enough to take his side to a win as Ruben Loftus-Cheek missed his kick from the spot in the penalty shootouts, giving Arsenal the victory.More news: Demi Lovato to leave hospital this week
Morata was given a golden opportunity to double Chelsea's lead when Hudson-Odoi brilliantly beat Hector Bellerin in the box and was fouled, but the Spain striker's poor penalty was easily saved by Cech.
'Today, obviously I think I did well, ' Hudson-Odoi told Chelsea TV.
The 17-year-old has been one of Chelsea's standout performers during their pre-season tour and fans are urging Sarri to give the forward an extended run in the first team.
'I never said it (Aubameyang's arrival) was bad for me, only people in the press said it was bad, ' Lacazette he said.More news: Someone Stole The Swedish Crown Jewels, Escaped In A Speedboat
After Hudson-Odoi was put through by Jorginho's flawless pass, Cech got his hand to the shot before Shkodran Mustafi hooked the ball to safety.
Hudson-Odoi's audition for a starting spot in next weekend's Community Shield continued into the second half, as the youngster forced another save out of Cech and then played a part in winning a corner that Rudiger this time headed wide. Yet it was this pairing that didn't look comfortable against Chelsea's attack.
The Brazilian could be on his way out of Stamford Bridge after being linked with Real Madrid and Manchester United.
Chelsea boss Maurizio Sarri replaced Fabregas with Danny Drinkwater and sent on Andreas Christensen for David Luiz during the interval.More news: New study ignites debate over cost of 'Medicare for all'