The loss ends five-time major champion Swiatek's bid to become the first woman to win the tournament in the Southern California desert three times.
Elena Rybakina knocked out defending champion Iga Swiatek at Indian Wells on Friday to set up a clash against Aryna Sabalenka in the final.
But the top seed targeted world number 68 Niemeier's serve to grab the decisive break and with it the opening set, before surrendering serve early in the next only to hit back from 2-0 down to level at 5-5 before going on to seal the victory.
Tennis missed an opportunity to send a strong message to Moscow by failing to impose a blanket ban on players from Russia and its ally Belarus after the invasion of Ukraine, World No 1 Iga Swiatek said.
Holger Rune powered past Argentine qualifier Genaro Alberto Olivieri 6-4 6-1 6-3 on Saturday to reach the French Open fourth round.
Defending champion Iga Swiatek made it to her third final in four years at Roland Garros.
Italian seventh seed Jannik Sinner beat Tommy Paul to set up a Canadian Open final clash with Australia's Alex De Minaur
Seven-times champion Novak Djokovic scored his 100th match win at Wimbledon and led the march of the old guard into the last 16 on Saturday while an ailing Barbora Krejcikova's title defence ended in defeat and tears.
Daniil Medvedev jumped for joy in an uncharacteristically emotional celebration after holding off young Frenchman Arthur Fils for a 6-4, 2-6, 7-6(7) win amid gusting winds on centre court in quarter-finals of the BNP Paribas Open, at the Indian Wells Tennis Garden, on Thursday.
Iga Swiatek will have her task cut out as she aims to pick up her third title in four years in Paris.
World number one Carlos Alcaraz faces a potential quarter-final clash with old foe Jannik Sinner in his US Open title defence, and American Coco Gauff is on a collision course with defending champion Iga Swiatek on the women's side.
The Pole, who won the crown in 2020 and hasn't lost since February, matched Serena Williams's winning run from 2013 in the process, having now lost only two sets in her last four tournaments.
Those not familiar with seeing Swiatek close up can expect to see her sliding on Wimbledon's grass, as she does on the clay
Alcaraz outlasts Hurkacz, Ruud stunned at Canadian Open
Poland's Iga Swiatek will take over the world number one ranking in style after keeping her remarkable winning run intact with a 6-4, 6-0 win over Japan's Naomi Osaka in the Miami Open final on Saturday.
Novak Djokovic said a majority of players believe favouritism is at play in the tennis anti-doping system.
Belinda Bencic won two tiebreaks to beat teenage Russian seventh seed Mirra Andreeva
Germany's Tatjana Maria was named the Comeback Player of the Year after reaching her first Grand Slam semi-final at Wimbledon after missing three majors last year due to the birth of her second daughter.
Madison Keys was dumped out of the Miami Open third round on Sunday, falling 6-4, 6-2 to Philippine wild card Alexandra Eala
Iga Swiatek is dynamite on court and the fireworks have just started, her coach Tomasz Wiktorowski said on Saturday after the world number one clinched her second Grand Slam title at the French Open.
Former French Open winner Jelena Ostapenko said the partisan fans at the Qatar Open were disrespectful for jeering her throughout her quarter-final match, as she eased to a 6-2, 6-2 win over Ons Jabeur.
The world number three has won eight out of her last nine matches on outdoor red clay, losing only to world number one Aryna Sabalenka in the Madrid Open final.
Iga Swiatek said she was "overwhelmed" after finding out Poland and Bayern Munich striker Robert Lewandowski was in attendance
World number one Iga Swiatek beat Tunisia's Ons Jabeur 6-2, 7-6(5) in the US Open final on Saturday to claim her maiden trophy at Flushing Meadows and third Grand Slam title.
Factbox on American second seed Coco Gauff, who defeated Belarusian world number one Aryna Sabalenka
IMAGES from the French Open women's final played at Roland Garros on Saturday
IMAGES from all the action on Day 7 of the US Open played at the USTA Billie Jean King Tennis Center at Flushing Meadows in New York on Sunday.
Iga Swiatek clinched her second French Open title after defeating American teenager Coco Gauff
Top-ranked Iga Swiatek cruised past Veronika Kudermetova in the semi-final of the Madrid Open to set up a second straight final showdown with world number two Aryna Sabalenka.
Coco Gauff was dumbstruck after beating world number one Aryna Sabalenka in the French Open final on Saturday
13 of the men's seeds fell at the first hurdle -- a Wimbledon record since 32 seeds were introduced in 2001.
'I always had this vision that we would all play until we are 35 or something'
* Swiatek started playing tennis in an attempt to emulate her older sister, who competed briefly on the junior circuit.
Images from Day 7 of the 2024 Australian Open in Melbourne on Saturday.
At an oven-like Centre Court where the temperature climbed to 30 degrees Celsius, Sabalenka twice rushed to the aid of ill fans by supplying bottles of cold water and an ice pack, before she cracked under pressure from her opponent in the 10th game.
Defending champion Aryna Sabalenka and Madison Keys made rocky starts on Thursday but eventually secured contrasting victories to set up a heavy metal Australian Open final showdown
Sabalenka, who has never reached the final at Roland Garros, believes she is now better equipped both physically and mentally to challenge on clay, a surface she concedes took her years to master.
Coco Gauff beat defending champion Iga Swiatek 6-3 6-4 at the WTA Finals in Riyadh on Tuesday to reach the semi-finals and ensure Aryna Sabalenka would finish the year as world number one.
A summary of Thursday's action at the US Open.
