West Ham's week of controversy ended with some relief after Craig Dawson scored a late equaliser to earn a 2-2 draw against Leicester after Kurt Zouma pulled out in the warm-up at King Power Stadium.
Dawson salvaged a point in the first minute of time added on after Jarrod Bowen put the Hammers ahead, but Youri Tielemans' 45th-minute penalty equalised before Ricardo Pereira's header appeared to clinch Leicester's first win in five in all competitions.
Zouma was reported to be feeling sick and suffered problems with his vision and substitute Issa Diop started instead with Irish international goalkeeper Darren Randolph making up the bench.
His withdrawal came after he was pictured on a video on social media kicking his pet cat.
The French centre back has been fined two weeks' wages, around stg£250,000, while two cats have been removed from his property and the RSPCA have launched an investigation.
Moyes explained after the game: "He was ill before the game, but he was desperate to play, and we wanted him to play.
"He was sick during the night - he stayed away from the players and didn't eat much.
"He didn't eat with us and he stayed away from the meeting.
"Once he got out there he didn't think it was possible. It is a stomach bug - probably from something he has eaten.
"We told Issa Diop to be ready and he played really well."
Moyes insists his side can compete for a Champions League place after it looked like they were going to lose until Dawson's goal, which came off his upper arm.
"It says lots for the players," he added. "I will squeeze everything out of them and I want us to challenge the top teams."
West Ham seemed unaffected however and settled quickly before taking a 10th-minute lead.
Diop lofted the ball forward and Leicester's defence was caught napping as Bowen controlled before firing a left-footed drive across Kasper Schmeichel for his ninth Premier League goal of the season.
It was in-form Bowen's seventh goal in as many games, making it 12 in all competitions this season.
Leicester, short of confidence after three defeats in their last four including a hammering at Sky Bet Championship side Nottingham Forest in the FA Cup, struggled early on and supporters were quick to show their frustration with pockets of boos around King Power Stadium.
The home side gradually improved to lift their fans however.
Tielemans and Harvey Barnes were both off target with angled shots from distance as Leicester sought an equaliser.
That came in the 45th minute when they were awarded a penalty after Aaron Cresswell handled as he tried to head away James Maddison's corner on the edge of the six-yard box.
Tielemans confidently drove the spot kick low to the right of Lukasz Fabianski, who guessed correctly but was beaten by the power and accuracy of the shot.
Leicester began the second half with much more purpose than they started the first and soon put West Ham under pressure.
Barnes was the dangerman, with one of his several crosses leading to Leicester's second goal.
Patson Daka was fractionally too late sliding in to convert the winger's cross.
But Barnes' next delivery was bang on the money, as Ricardo beat Cresswell to plant a bullet header into the top corner of the net.
Tielemans flashed a rising shot just wide as Leicester sought a third goal.
But after Hammers substitute Said Benrahma produced two efforts, the visitors salvaged a point when Bowen's corner went in off Dawson's upper arm, looping high into the net.
Leicester manager Brendan Rodgers felt for his players after they conceded a 14th goal from a set-piece this season, while five of their last seven have come in the last five minutes of matches.
"I really feel for the players because that feels really deflating when we have conceded from a set-piece again," said Rodgers.
"We've had a few of them lately, and it was hard for the players.
"There was anxiety there but possession is a mantra - you have to take the ball and be brave."
Rodgers felt his side were back to their best during the second half.
"In the second half we were outstanding and in the first half West Ham were better," he added.
"The second half was like watching us of old, with the speed of the game and chances."
