Barrie McKay's goal and a stoppage-time Joe Garner header earned the Ibrox men three Premiership points after Kris Doolan's opener for Thistle.
Caixinha admitted the performance was "disorientated" but felt his players showed they are fighting for him.
"If we were not together as a group I don't think the players would celebrate like that at the end," Caixinha said.
"I really like the way the players understood and were committed. There were a lot of moments I really felt the passion from the players."
The result secured a top-four finish and European football for Rangers next season, but for much of the match they were second best to Alan Archibald's side.
Caixinha made a series of system and personnel changes, with substitute McKay making a big difference, but for long spells the Ibrox men struggled to get into any sort of rhythm.
The manager, however, defended his changes as his side responded to back-to-back Old Firm defeats.
"Today was really important for us to show a reaction," he added. "We showed it in the second half and I need to be happy with that.
"We needed to change the course of the game and we managed it.
"My passion and dedication to this sport is that I would rather die trying it rather than be alive to see what happens. And that is what the players did."
Jags boss Archibald was left to explain another late collapse against Rangers. In November at Firhill the Jags had taken the lead only for a late Joe Dodoo double to win it for the Ibrox men.
"It's a sore one," he said. "We put a lot into that first-half performance. We created a number of good opportunities - that was the only negative, not adding to our 1-0 lead.
"We weren't outdone by tactics or anything like that. It's one long ball that outdoes us.
"You feel guilty about having a go but we've got to learn from it. We've got to move on. We want to be a top-six side, we want to stay away from the bottom end of the league. You've got to see games out and manage them and learn from it.
"Once we lost the goal we didn't react in the right way. We didn't do the basics.
"With 30 seconds to go, you've got to go and defend your box as if your life depends on it."
Pedro Caixinha insists his Rangers players proved their commitment in the comeback win at Partick Thistle.