Monfils did it the hard way, as he suffered an early injury scare during the clash against Dellien and then went two sets to love down before producing some magic to claim a 4-6, 3-6, 6-1, 7-6 (7-4), 6-1.
Playing in the evening match on Court Philippe-Chatrier, Monfils crashed into the advertising boards during the first set and asked for a medical timeout for treatment to his hand, knee and back.
He battled on, but soon found himself staring defeat in the face as Dellien won the opening two sets.
But then he pulled out some typical Monfils magic as he won the third set and then overcame an early mini break in the tie-breaker in the fourth set to take it to a fifth set.
The Frenchman then dominated the decider to claim a 12th five-set win at Roland Garros, which is a new Open Era French Open record.
“It’s difficult to express. It’s really magic,” the world No. 42 said after the three-hour and 36-minute encounter.
“It’s strange, but there’s this point which was incredible for the match, this passing shot. I tried something. I thought I was going to lose the point. I thought this was over. I hit a winner. I had to dare.
“That is magic. You go for it and, boom, you succeed.”
The 38-year-old added: “I feel like the belief, the belief of myself, the belief that even I’m down, I need to find the solution.
“I think I have also even more here [at Roland Garros] but I have to find the solution, have to find the solution.
“I keep fighting with the opponent, with my thoughts also because it is never easy also in your mind.
“To be honest, for me it is the belief, the belief in myself. I know at Roland Garros is a little bit different, so I even push more.”
But that was not the only milestone that Monfils achieved on the night as he is now also the joint-record holder for the most match wins by a Frenchman at Roland Garros.
His win over Dellien was his 40th at his home Grand Slam and he is now top of the list with the legendary Yannick Noah.
Richard Gasquet, who will bow out after this year’s French Open, sits third on 31 wins with Jo-Wilfried Tsonga (28), Henri Leconte (27) and Francois Jauffret (27) completing the top five.
“I won 40 times here?” he asked. “It means I’ve played for a long time, that’s probably the reason why.”
He will have a chance to move to 41 match wins at Roland Garros when he takes on fifth seed Jack Draper in the second round.