Monfils, the world No 81, prevailed 7-6 (10/8), 6-4, 6-7 (3/7), 6-7 (4/7), 7-5 in front of an ecstatic Court Philippe Chatrier crowd after four hours three minutes.
The Frenchman, who reached the semi-finals at Roland Garros in 2008 and missed last year's event because of a knee injury, wrapped up the match with his fourth match point when Berdych sent a backhand long.
He will next face Latvia's Ernests Gulbis.
Meanwhile, defending women's champion, Maria Sharapova, was not distracted by a late court switch as she started her French Open title defence with a ruthless 6-2, 6-1 dismissal of Taipei's Hsieh Su-Wei in the first round.
With the encounter between Monfils and Tomas Berdych dragging on over on Court Philippe Chatrier, the Russian second seed's match was moved to the Suzanne Lenglen arena where Sharapova enjoyed a 54-minute stroll.
She ended her opponent's ordeal with a crosscourt backhand winner, with some spectators having barely had time to sit down.
Sharapova next faces Canada's Eugenie Bouchard.
French Open results on Monday (x denotes seeded player):
Men:
First round:
John Isner (USA x19) bt Carlos Berlocq (ARG) 6-3, 6-4, 6-4
Rafael Nadal (ESP x3) bt Daniel Brands (GER) 4-6, 7-6 (7/4), 6-4, 6-3
Martin Klizan (SVK) bt Michael Russell (USA) 3-6, 6-3, 6-1 - retired
Lukás Rosol (CZE) bt Pere Riba (ESP) 6-3, 6-4, 6-4
Fabio Fognini (ITA x27) bt Andreas Beck (GER) 6-3, 7-5, 6-3
Grega Zemlja (SLO) bt Santiago Giraldo (COL) 6-1, 6-4, 6-1
Kei Nishikori (JPN x13) bt Jesse Levine (CAN) 6-3, 6-2, 6-0
Robin Haase (NED) bt Kenny De Schepper (FRA) 6-4, 7-6 (7/3), 2-6, 6-3
Jerzy Janowicz (POL x21) bt Albert Ramos (ESP) 7-6 (7/3), 7-5, 6-3
Michal Przysiezny (POL) bt Rhyne Williams (USA) 6-3, 6-7 (5/7), 7-5, 7-5
Richard Gasquet (FRA x7) bt Sergiy Stakhovsky (UKR) 6-1, 6-4, 6-3
Gael Monfils (FRA) bt Tomas Berdych (CZE x5) 7-6 (10/8), 6-4, 6-7 (3/7), 6-7 (4/7), 7-5
Ernests Gulbis (LAT) bt Rogério Dutra Silva (BRA) 6-1, 7-6 (7/4), 6-3
Igor Sijsling (NED) bt Jurgen Melzer (AUT) 6-4, 6-3, 6-2
Tommy Robredo (ESP x32) bt Jurgen Zopp (EST) 6-3, 6-2, 6-1
Edouard Roger-Vasselin (FRA) bt Martín Alund (ARG) 6-2, 4-6, 6-1, 6-0
Nicolas Almagro (ESP x11) bt Andreas Haider-Maurer (AUT) 4-6, 6-4, 6-3, 6-3
Evgeny Donskoy (RUS) bt Jan-Lennard Struff (GER) 7-6 (9/7), 2-6, 7-6 (7/2), 6-2
Feliciano Lopez (ESP) bt Marcel Granollers (ESP x31) 7-5, 2-6, 6-4, 4-6, 6-4
Albert Montañés (ESP) bt Steve Johnson (USA) 6-4, 3-6, 6-3, 3-6, 6-1
Jo-Wilfried Tsonga (FRA x6) bt Aljaz Bedene (SLO) 6-2, 6-2, 6-3
Jarkko Nieminen (FIN) bt Paul-Henri Mathieu (FRA) 6-4, 4-6, 7-6 (11/9), 4-6, 6-2
Daniel Gimeno (ESP) bt Juan Monaco (ARG x17) 4-6, 4-6, 7-6 (7/4), 6-4, 6-4
Nick Kyrgios (AUS) bt Radek Stepanek (CZE) 7-6 (7/4), 7-6 (10/8), 7-6 (13/11)
Marin Cilic (CRO x10) bt Philipp Petzschner (GER) 6-1, 6-2, 6-3
Pablo Cuevas (URU) bt Adrian Mannarino (FRA) 6-3, 2-6, 6-3, 5-7, 7-5
Julien Benneteau (FRA x30) bt Ricardas Berankis (LTU) 7-6 (7/5), 6-3, 5-7, 7-6 (7/5)
Tobias Kamke (GER) bt Paolo Lorenzi (ITA) 6-3, 6-3, 3-6, 0-6, 6-3
Women
First round
Johanna Larsson (SWE) bt Monica Niculescu (ROM) 6-2, 6-3
Roberta Vinci (ITA x15) bt Stéphanie Foretz (FRA) 6-3, 6-0
Caroline Wozniacki (DEN x10) bt Laura Robson (GBR) 6-3, 6-2
Bojana Jovanovski (SRB) bt Barbora Záhlavová Strýcová (CZE) 6-3, 6-2
Magdaléna Rybáriková (SVK) bt Pauline Parmentier (FRA) 6-0, 6-1
Svetlana Kuznetsova (RUS) bt Ekaterina Makarova (RUS x22) 6-4, 6-2
Varvara Lepchenko (USA x29) bt Mirjana Lucic (CRO) 6-1, 6-2
Elina Svitolina (UKR) bt Romina Oprandi (SUI) 6-3, 4-6, 6-1
Jana Cepelová (SVK) bt Christina McHale (USA) 7-6 (7/3), 2-6, 6-4
Angelique Kerber (GER x8) bt Mona Barthel (GER) 7-6 (8/6), 6-2
Agnieszka Radwanska (POL x4) bt Shahar Peer (ISR) 6-1, 6-1
Zuzana Kucová (SVK) bt Julia Görges (GER x24) 7-6 (10/8), 6-0
Mathilde Johansson (FRA) bt Chanelle Scheepers (RSA) 7-5, 6-1
Madison Keys (USA) bt Misaki Doi (JPN) 6-3, 6-2
Carla Suárez (ESP x20) bt Simona Halep (ROM) 3-6, 6-2, 6-2
María Teresa Torró (ESP) bt Julia Glushko (ISR) 6-2, 7-5
Li Na (CHN x6) bt Anabel Medina Garrigues (ESP) 6-3, 6-4
Bethanie Mattek-Sands (USA) bt Lourdes Domínguez (ESP) 6-4, 6-1
Paula Ormaechea (ARG) bt Tatjana Malek (GER) 6-3, 4-6, 6-0
Francesca Schiavone (ITA) bt Melinda Czink (HUN) 6-0, 7-6 (7/1)
Garbiñe Muguruza (ESP) bt Karolína Plísková (CZE) 4-6, 7-5, 6-3
Vania King (USA) bt Alexandra Cadantu (ROM) 7-6 (7/3), 6-1
Sloane Stephens (USA x17) bt Karin Knapp (ITA) 6-2, 7-5
Melanie Oudin (USA) bt Tamira Paszek (AUT x28) 6-4, 6-3
Zheng Jie(CHN) bt Vesna Manasieva (SRB) 6-4, 6-1
Eugénie Bouchard (CAN) bt Tsvetana Pironkova (BUL) 6-1, 7-6 (7/2)
Maria Sharapova (RUS x2) bt Hsieh Su-Wei (TPE) 6-2, 6-1
Kirsten Flipkens (BEL) bt Flavia Pennetta (ITA) 2-6, 6-4, 6-0