Before Wednesday's potentially explosive stage, man-to-beat Tadej Pogacar protected his 33-second overall lead over Remco Evenepoel with defending champion Jonas Vingegaard at 1min 15sec in third.
Last year's green jersey winner Philipsen closed the gap slightly on current occupant Girmay, who has two stage wins and 267 points to the Alpecin-Deceuninck rider's 193.
Philipsen was guided to victory by team-mate and world road race champion Mathieu van der Poel.
"When you have a world champion to lead you out in your Tour de France sprint it is magnificent," said Philipsen after hitting a speed of 75km/h (46.6 mph).
After Monday's rest day the 172 remaining riders embarked from the city of Orleans past the statue of Jeanne d'Arc and the historic city's giant cathedral.
Low balmy skies and a temperature of 28 degrees Celsius (82 degrees Fahrenheit) persuaded the bunch to pace themselves across the vast wheat plains to the south of Orleans.
Relaxing run
It was slow enough for Briton Tom Pidcock to unwrap a sandwich from silver foil, while beside him Pavel Sivakov spotted the open door of a camping car and gracefully launched his water bottle through it.
In the battle for the overall title the so-called Fab Four of Pogacar, Evenepoel, Vingegaard and Primoz Roglic are locked in a tense and tetchy struggle at this halfway stage 10 with no obvious favourite.
In his Giro d'Italia-Tour double bid Pogacar may have expected to be further ahead given how much effort he has invested.
Evenepoel looks fresh and calm and is giving off a far happier vibe than the three others.
Two-time winner Vingegaard is riding into form and winning a war of nerves as he tails Pogacar relentlessly, but has suffered an early blow with the 1min 15sec deficit.
Pogacar's compatriot Roglic is waging a dark horse run in fourth at 1min 36sec but is priming his form for week three.
Any hopes of a record-extending 36th stage win for Mark Cavendish dissolved when he lost his sprint train on a tight corner in the final kilometre.
At the same finish line on stage 13 of the 2013 Tour, 39-year-old Cavendish managed to cross an echelon in strong winds, but on Tuesday he was outside the chase at the finale.
Wednesday's 211km ride continues south but through dormant volcanic mountains including a handful of testing climbs to the west of the city of Clermont.
