He claimed maximum bonus points from the power stage and, after finishing second in the season-opening Rally Monte-Carlo, holds a four-point lead in the drivers' standings.
It is the first time any driver other than four-time champion Sebastien Ogier has led the championship since February 2014.
"It's amazing. A new team, a new car, our second rally and we're winning. I have no words to describe it, I'm so emotional," Latvala said. "We're at a good level but now we go forward and it gets more difficult.
"Mexico is next up and I'm really motivated for the championship."
Paddon struggled early on the opening day before finding his rhythm late in the day. A power-steering failure saw him drop further back on Saturday but he posted top five times on the final day and collected a power stage bonus point.
"Certainly, it's been a trying weekend," the 29-year-old said. "We always knew it was going to be tough coming here after Monte, and certainly underestimated that challenge.
"So, to get to the finish, I must admit, releases the pressure a little bit.
"I certainly feel a lot more relaxed and more back to normal, if you like, going forward towards to Mexico. To get a few points amongst all our difficulties this weekend at least gets us on the board.
"We know where we can improve. We know can build on the confidence. We've got a good two-day test ahead now to prepare for Mexico and get back onto the gravel. So not all lost, we're just looking forward now.
"A long way to go in the season, 11 rallies. We know where we're missing the speed, so that's what we'll focus on now and make sure we have a good two-day test and develop the car to work for myself a bit better."
Final standings
1. Jari-Matti Latvala (Toyota)
2. Ott Tanak (Ford) +29.2s
3. Sebastien Ogier (Ford) +59.5s
4. Dani Sordo (Hyundai) +2:11.5s
5. Craig Breen (Citroen) +2:51.2s
6. Elfyn Evans (Ford) +5:26.6s
7. Hayden Paddon (Hyundai) +5:31.2s
8. Stephane Lefebvre (Citroen) +7:14.7s
