Unbeaten in six, Palace made one change from the side who ran out 1-0 victors at Ipswich on Tuesday, with Cheick Doucoure - who struggled against the Tractor Boys - replaced by Jefferson Lerma.
Glasner has been urging his Palace side to take their chances after scoring just 12 times this season, and they set off perfectly, taking the lead inside the first five minutes.
Will Hughes picked the ball up in midfield and threaded a perfectly timed pass through to Daniel Munoz. The Colombian had been released one-on-one with Stefen Ortega, taking advantage of the opportunity and drilling an effort past the City shot-stopper.
Goals had been hard to come by for Daniel Munoz in red and blue, but now the wing-back has scored twice in his last two games at Selhurst Park.
Both sides were landing blows early door; Manchester City looked for an instant response to Palace’s opener. Kevin De Bruyne fed an exquisite pass through to Erling Haaland in the seventh minute, but the latest member of the Premier League's hundred club, Dean Henderson, was on hand to produce a stunning save.
The Eagles, however, continued to play front-footed football. Eberechi Eze was enjoying space in the middle of the park and dropping threatening balls over the top of the City backline.
Attack was proving the best form of defence for Palace, with the hosts playing penetrative football through the City midfield.
Chances were coming and going for Palace, but nonetheless, they were going toe-to-toe with Pep Guardiola’s Champions.
City had another opening to pull back level when Ilkay Gundogan struck the post from his left-footed effort inside the box. Despite City going close on a couple of occasions, it was Palace who were crafting the better chances.
The hosts embarked on another promising attack in the 29th minute, playing quick football to reach the City box. Pass, pass, pass - it was calling out for someone to take a shot. Eventually, Jefferson Lerma riffled an effort towards the City net, but Ruben Dias was able to block. Too much hesitation cost Glasner’s side.
Two minutes later, Palace rued their missed chances when Mathues Nunes launched a looping cross towards the back post. Haaland was on hand to leap higher than Marc Guehi and nod his side level.
_(Image: PA)_For Glasner and his side, the final 15 minutes of the first half dragged as City began to climb on top. Nonetheless, Palace reached the halfway mark level with a pretty impressive display of football.
Since joining the South London club last season, Glasner instilled the mindset into his team that every game is there to be won. Removing the historic inferiority complex in SE25. The first half performance demonstrated exactly that. Palace were unafraid to take the game to Guardiola’s side and they deservedly led for 26 minutes.
Palace found it difficult to live up to their creativity in the first ten minutes after the break. Most of the football was being played in the hosts defensive half and City were on top without really threatening.
Though, the South London club were not going to remain quiet for long. Will Hughes stood over a corner after Palace put together their first attack of the half. The delivery was inch perfect. Maxence Lacroix towered over the City defence and fired a bullet header past Moreno, putting Palace ahead with his first goal in red and blue.
However, Palace's lead was not to last. City's quick football opened up the Palace defence before Rico Lewis ran free into the box, received the ball and launched it into the top corner, leaving Henderson hopeless in goal.
After drawing level for the second time, Guardiola's side had the scent - they could smell victory. The Citizens were pushing, and Henderson was forced to make a crucial stop to deny Savinho.
Youngster Justin Devenny was introduced for his toughest test yet in a Palace shirt, with Eze making way for the Northern Ireland international, while Eddie Nketiah replaced Ismaila Sarr shortly after.
Palace's exhibition had gone from a classy one to a battling one. Showing heart and desire to stick with the Citizens.
Will Hughes had been an animal in midfield. Jean-Philippe Mateta was a workhorse up top. Daniel Munoz a weapon at wing-back. That's not to mention Maxence Lacroix's and Jefferson Lerma's impressive outings. All over the pitch, Palace had been excellent.
With five minutes left on the clock, a late blunder from Lewis gave Palace a chance to snatch all three points. The England international, who had not long brought the visitors level, left a late lunge on Trevoh Chalobah, with the referee brandishing the 20-year-old with his second yellow card.
Palace showed glimmers. Nketiah had a four-on-two situation, which faded. Devenny had an effort inside the box. While the Eagles had two corners in stoppage time that they failed to take advantage of.
The referee called curtains on an entertaining affair when the clock hit 94 minutes with the spoils shared. On balance, it was probably a fair result - both sides had an abundance of chances.
For Palace, they continue their positive start to the festive period with their best performance of the season, claiming a point against Manchester City.