Humbert trailed 2-5 in the second set and faced the match points at 3-5, then turned things around to clinch a 6-7 (4), 7-6 (5), 7-6 (5) win after nearly three hours.
Andy Murray squandered a set point in the opening set before losing 6-7 (8), 1-6 to the 83rd-ranked Egor Gerasimov
Lille need only a draw at home to mid-table Brest on Sunday to reclaim first place.
Kylian Mbappe scored twice and Mauro Icardi was also on target with PSG leading 1-0 before netting three times in the space of four minutes around the hour mark.
Kevin Volland and Ben Yedder netted within an hour before Elye Wahi and Andy Delort clawed Montpellier back into the game
European football matchday: AS Roma visit Lazio in capital derby; Leverkusen away at surprise package Union Berlin
AS Roma are third in the standings, three points behind Inter Milan and six below league leaders AC Milan.
Defending champion PSG beat Strasbourg 4-0 in an otherwise uninspired performance that saw the home side benefit from three late goals amid sloppy defending from the visitors.
Marseille moved up to second in the French league, one point behind defending champion Paris Saint-Germain.
Di Maria struck in each half, with Moise Kean scoring the other, to move PSG up to 24 points, five ahead of second-placed Lille who take on Brest in Sunday's early fixture.
Memphis Depay scored what might be his farewell goal for Lyon on Tuesday in a 2-1 Ligue 1 defeat at Montpellier which could be his final match before a rumoured move to Barcelona.
Montpellier's defense kept Nice striker Kasper Dolberg quiet while veteran center half Daniel Congré took care of scoring duties with two in a 3-1 win.
Ligue 1: Eduardo Camavinga's goal propels Rennes to win over Montpellier as both teams see red; Nice beat Strasbourg
Rennes teenager Eduardo Camavinga celebrated his first France call-up with a terrific solo goal in Saturday's 2-1 victory at home to Montpellier in Ligue 1.
Marseille, who had to cancel what would have been the Ligue 1 season opener last Friday because of the five existing coronavirus cases, added that they had notified the French league about the new infections.
Ligue 1: Bordeaux appoint veteran Jean-Louis Gasset as head coach after parting ways with Paulo Sousa
Gasset was assistant to Laurent Blanc when Bordeaux won the French top flight in 2009.
Ligue 1: Rennes, Lille clinch victories at home to stay a point apart in race for last Champions league spot
Rennes and Lille both won at home on Sunday to stay one point apart in the race for third place in the French league.
Kylian Mbappe capped a brilliant individual performance by scoring twice and creating another for Mauro Icardi as leaders Paris St Germain cruised to a comfortable 4-0 victory over Dijon in their Ligue 1 clash at the Parc des Princes
Ligue 1: AS Monaco beat visitors Montpellier for third consecutive win; Paris Saint Germain visit Amiens
In the weekend’s standout fixtures, champions and runaway league leaders Paris St Germain visit second-bottom Amiens on Saturday
Rotterdam Open 2020: Defending champion Gael Monfils beats Dan Evans in straight sets to advance to semi-finals
Monfils will meet Serb Filip Krajinovic or Russian seventh seed Andrey Rublev, while Spain’s Pablo Carreno Busta faces Canadian teenager Felix Auger-Aliassime in the other semi-final
Ligue 1: Edinson Cavani scores as PSG beat Lyon to restore 12-point lead atop league table; Montpellier defeat Saint-Etienne
PSG overcame another shaky performance in defense to beat Lyon 4-2 on Sunday and restore its 12-point lead over second-place Marseille
Ligue 1: Kasper Dolberg strikes twice in Nice's win over Lyon; second-placed Marseille falter as PSG increase lead to 12 points
The first league defeat for Lyon this year left both clubs on 32 points, far behind league leader Paris Saint-Germain