Gardner Minshew II speaks with Scott Van Pelt after his two-touchdown performance against the Titans, saying he is earning trust after every snap. (1:27)

JACKSONVILLE, Fla. -- Not only is Gardner Minshew capably filling in for the injured Nick Foles, but the rookie sixth-round pick is beginning to show he might be able to carry the Jaguars' offense.

The Jaguars' run game was essentially nonexistent Thursday night against the Tennessee Titans until late in the fourth quarter, so it was all on Minshew. He delivered with two touchdown passes and two other scoring drives to lead the Jaguars to a 20-7 victory at TIAA Bank Field.

"I think we're all building trust right now," Minshew said. "Whether it's me and Flip [offensive coordinator John DeFilippo] ... or me and the guys on the field, all I can do is try to earn that trust every day, and I think when you do that you get more opportunities to do fun things."

Things like beat a Titans team that had won four in a row in the series and had embarrassed the Jaguars in their previous two national television appearances. It was Minshew's first victory as a starting quarterback and the Jaguars' first victory of the season, and it came on a short week filled with a massive distraction: cornerback Jalen Ramsey asking the team to trade him.

Minshew completed 20 of 30 passes for 204 yards and wasn't intercepted. He has completed 74% of his passes in his three games, the highest completion percentage of any quarterback through his first three career games since 1970. Interestingly, No. 5 on that list is former Jaguars starter Blake Bortles (67%).

"A lot of people never thought I would get this opportunity, so now that I do have it, I make the most of it," Minshew said. "I'm super grateful for it, but I know through everything I've learned in my career, with the situation I'm in, I know I may only get one, so you gotta make the most of it. So that's what I'm trying to do now."

The Jaguars' run game has been a disappointment this season, mainly due to a lack of production in the middle of the offensive line. The Jaguars had 19 yards rushing through three quarters, thanks largely to Minshew's 18 yards on four carries. Leonard Fournette had minus-3 yards on nine carries. He finished with 66 yards, thanks to a 69-yard run late in the fourth quarter.

Minshew threw both of his touchdown passes in the first quarter, making him just the second rookie to throw two scoring passes in the first 10 minutes of a game in the past 10 seasons. The only other rookie to do so was Tennessee's Marcus Mariota, during his NFL debut in 2015.

With five touchdown passes and only one interception, Minshew is the second quarterback in franchise history to throw a touchdown pass in each of his first three games. Byron Leftwich did it in 2003.