Meanwhile, Leicester, who were strong favourites to finish third at the turn of the year, lacked a cutting edge throughout and are now looking over their shoulders at fourth-placed Chelsea – who visit the King Power Stadium in the FA Cup quarter-finals this weekend.
Brighton began brightly with a flurry of efforts, all of which were repelled by the Leicester defence.
Their early endeavour looked like it would be rewarded after Aaron Connolly chased a long pass forward by Aaron Mooy and was clumsily brought down by James Justin.
The Video Assistant Referee checked the penalty decision but referee Lee Mason’s award of the spot-kick stood, only for Schmeichel to save from Maupay.
It was a let off for Leicester but a poor penalty from the Brighton striker, with Schmeichel not needing to stretch or extend himself to keep it out.
Brighton, who had to make a change at centre-half with Shane Duffy replacing the injured Adam Webster, threatened again through Connolly midway through the first half when he once more broke through the heart of the Leicester defence, but his effort was deflected wide by the recovering Caglar Soyuncu.
Some nice play from Leicester creates a chance for James Maddison but his effort sails high and wide! 💥
Leicester offered little in the first half, with Jamie Vardy and Kelechi Iheanacho largely anonymous and starved of service.
However, they could have taken the lead in injury time but Soyuncu got his header from close range all wrong after a Wilfred Ndidi shot looped towards him at the far post.
The hosts looked a little more lively as the second half got under way and Ben Chilwell, on the scoresheet in the 1-1 draw at Watford on Saturday, spurned a good chance.
Vardy headed the ball back across goal and Brighton failed to clear it properly, allowing Chilwell a strike at goal, but the left-back snatched at his chance.
Another Vardy lay-off sat up invitingly for James Maddison to strike but he too rushed his effort and fired his 25-yard shot wide.
Brighton’s menace had waned, despite boss Graham Potter freshening things up with a triple substitution just before the hour mark, but Leicester were unable to make their growing possession stats tell on the scoreboard.
Maddison, regularly lethal with free-kicks just outside the penalty area, put the ball in the empty stands again with 10 minutes left.
Brighton get a penalty early on! 🔵⚪
Aaron Connolly gets the better of James Justin and a spot-kick is awarded - correct decision? 🤔
He said: “I didn’t think we were very good in the first half. We got into some good positions, but didn’t have very good movement off the ball. Kasper made a good stop from the penalty.
“I thought second half we were much better. It felt like it was coming, but we didn’t quite make the final pass. A clean sheet, fitness was good and subs tried to make an impact and we didn’t concede so we’ll take a point.
“We haven’t won the games, but we’ve showed a good mentality to not concede so much and hopefully after more training we can find the goals to get back to winning.”
Meanwhile, Graham Potter praised the fight of his side after they backed up Saturday’s 2-1 win over Arsenal with a goalless draw at Leicester.
“Four points from two games is good, especially when you consider the opposition, but every game is tough,” he said. “We have to fight for every single point.
“We carried a threat in the first half, the penalty is a big moment for us, but we carried a threat. We had to dig in at times and overall a clean sheet, I am really proud of the players.
“To be able to stick together like they did and push until the end was fantastic. We had to defend more in the second half, but we were still OK.”