The 25-year-old Dzumhur recovered from a poor start to beat the Briton 1-6, 7-5, 6-3 and will bid to become the Balkan nation's first Tour winner in Saturday's title-decider against Spain's Roberto Bautista Agut.
Defending champion Federer, battling a flu bug according to the local media, was made to work hard by his Bulgarian opponent before the Swiss master prevailed 6-4, 6-7(4), 6-4 at the Pat Rafter Arena. "It was tough. Grigor's a great shotmaker, the future's ahead of him in the game," Federer said after setting up a semi-final against Austrian youngster Dominic Thiem.
Wimbledon champion Garbine Muguruza notched up her first ever victory on Arthur Ashe Stadium with a 6-0, 6-3 win over American Varvara Lepchenko at the US Open on Monday.
A few days after it appeared as though a Roger Federer impersonator had gatecrashed the 02 Arena, the Swiss great resumed normal service to outplay Kevin Anderson and reach the last four of the ATP Finals on Thursday.
It was the 31-year-old Serb's second comfortable win in the Gustavo Kuerten group and combined with Marin Cilic's 6-7(2), 6-3, 6-4 defeat of American John Isner later in the day, he sealed his place in the semi-finals at the year-ender for the eighth time.
Croatia's Ivo Karlovic became the oldest ATP winner since Jimmy Connors in 1989.
As another Grand Slam crown looks set to be snaffled by a man in his thirties this weekend, tennis fans lamenting a dearth of dynamic up-and-comers need not worry, says former world number one Mats Wilander.
With temperatures reaching almost 38 degrees on court, Murray, a twice Wimbledon champion, was beaten 7-6(4), 6-2 by Australian world number 90 Jordan Thompson.
IMAGES from matches played at the Miami Masters in Key Biscayne, Florida
Only one player has beaten Rafael Nadal on his beloved claycourts this year and that man, Austria's Dominic Thiem, blocks the Spaniard's path to the French Open final.
Federer, who skipped the entire clay court season after winning the Australian Open and claiming titles at Indian Wells and Miami this year, will next play defending champion Florian Mayer who beat Frenchman Lucas Pouille in three sets.
Cilic's booming serve lacked its usual accuracy and Germany's Kohlschreiber was able to control long rallies, pushing the towering Croatian around the court with pinpoint groundstrokes en route to a quick victory.
The latest tennis rankings have been announced by the ATP and WTA
Images from the matches played on Day 7 at the Roland Garros on Saturday
Benoit Paire made a remarkable Davis Cup debut for France, outplaying Pablo Carreno-Busta 7-5, 6-1, 6-0 in the opening rubber of the World Group semi-final tie against Spain at the Stade Pierre-Mauroy on Friday.
Images from Day 5 of the French Open in Paris on Thursday.
A summary of sports events and sports persons, who made news on Tuesday
Andy Murray's preparations for the US Open got off to a poor start when the Briton suffered a stunning loss.
The 36-year-old was all over the world number 58 throughout a one-sided contest under the Rod Laver Arena roof, breaking three times to win the opening set in 33 minutes.
Edmund is no flash Harry, on or off the court
Defending champions Rohan Bopanna and Jeevan Nedunchezhiyan were ousted from the Tata Open Maharashtra but Yuki Bhambri and Divij Sharan combined to shock the top seeds, keeping the Indian hopes alive, in Pune, on Thursday.
Making a stupendous start to the fresh season, Ramkumar Ramanathan scalped higher-ranked Roberto Carballes Baena to set up a second round clash with tournament-favourite Marin Cilic at the inaugural Tata Open Maharashtra, in Pune.
Both won in style on Sunday, with Spanish fifth seed Nadal pouncing on Guido Pella's serve to break the Argentine five times en route to a 6-3, 6-2 victory in sizzling afternoon heat on the stadium hard court.
The top women's seeds continued to be scattered at Wimbledon on Wednesday, with Caroline Wozniacki's exit meaning five of the top eight were gone before the end of the third day.
Nothing that has happened in the past 12 months suggests Roger Federer's hunger is diminished with victory at this year's Australian Open taking his Grand Slam title haul to 20.
The Swiss squandered seven set points in the opener and although he took the second on a tiebreak he capitulated in the decider after dropping serve at 1-2, losing 7-5, 6-7(3), 6-1.
Nicolas Mahut and Pierre-Hugues Herbert made sure of that with a gripping doubles win that keeps France's hopes against Croatia alive in the last final to be staged in the event's traditional format.
Former world number one Rafael Nadal displayed more signs of a return to top form with a ruthless 6-2, 6-1 hammering of Stanislas Wawrinka to reach the semi-finals of the Shanghai Masters on Friday.
Team Europe swept the singles matches at the inaugural Laver Cup on Friday before Australian Nick Kyrgios and American Jack Sock took down top-ranked Rafael Nadal and Tomas Berdych in the doubles to salvage a point for Team World.
A summary of sports events and sports persons, who made news on Tuesday
Roger Federer made a comfortable start to his quest for a 100th title, despatching Fabio Fognini in straight sets to ease into the quarter-finals at the Paris Masters on Thursday.
'I feel happy to be part of this rivalry, but at the same time, I played even more matches with Novak (Djokovic) than with Roger in such important matches, too'
Novak Djokovic began his bid to hold on to his number one ranking with an easy win over Gilles Muller in the Paris Masters second round while Andy Murray struggled through and Stan Wawrinka faltered on Wednesday.
Indian Aces notched up their third win on the trot with a 28-20 victory over UAE Royals in the battle of two unbeaten sides in an India Premier Tennis League match in Manila.
US Open, the final Grand Slam of the season, starts Monday, August 28, at Flushing Meadows in New York.
A summary of sports events and sports persons, who made news on Thursday
Following Stanislas Wawrinka's win at the US Open on Sunday, it may finally be time to officially expand the 'Big Four' in men's tennis to the 'Big Five'.
It was his first victory ever against a player ranked in the top two and it avenged the semi-final loss at the Rio Olympics where Murray went on to win gold and Nishikori settled for bronze.
Lucas Pouille was not prepared to say his pulsating four hour, fourth-round upset of 14-time grand slam winner Rafael Nadal at the US Open on Sunday was a career changing moment.
Roger Federer is the oldest male player to win a Grand Slam title since Australia's Ken Rosewall won at Melbourne Park in 1972 at the age of 37.
