The 30-year-old Barcelona striker scored his 42nd and 43rd goals in the 79th and 80th minutes to give France a victory that moved it into first place in Group B with one game to play.
Sub Karim Benzema set up the first goal Henry knocked through a maze of players, and midfielder Jeremy Toulalan sprung Titi for the second goal.
"It really pleases me, especially as they are important goals," said Henry, who made his debut for France in 1997. "It's beyond me."
Henry dedicated the victory to his father.
"It was really not easy tonight," he said. "At one stage, I thought we would not make it. I thought of my father [when I scored]. He is not well at the moment. Without him, I would not be here. I will give this jersey to him."
FRANCE LEADING SCORERS
1. Thierry Henry, 43 goals, 96 caps
2. Michel Platini, 41 goals, 72 caps
3. David Trezeguet, 34 goals, 69 caps
4. Zinedine Zidane, 31 goals,108 caps
5. Just Fontaine, 30 goals, 21 caps
6. Jean-Pierre Papin, 30 goals, 54 caps
7. Youri Djorkaeff, 28 goals, 82 caps
8. Sylvain Wiltord, 26 goals, 92 caps
9. Jean Vincent, 22 goals, 46 caps
10. Jean Nicolas, 21 goals, 25 caps