Hosmer drilled a single to right field past Oakland second baseman Andy LaRoche in the fifth inning of the Royals' 4-3 victory on Saturday night.
The hit came at an opportune time because A's starter Brandon McCarthy had retired all 14 batters who came before Hosmer, who smacked a 2-1 fastball.
"If anything, it got us going a little bit," Hosmer said. "I'm just happy we won the game. It's a big sigh of relief to get the first one out of the way and just settle in now and keep going out and having fun."
The crowd of 25,828 at Kauffman Stadium gave him a standing ovation.
"That's unbelievable," Hosmer said. "The last two days the crowds have been unreal, and these guys make it comfortable for you to come in here every day and play."
Hosmer narrowly missed his first hit in the second inning when he whistled a line drive toward the left-center field gap. Unfortunately for the Royals, left fielder Josh Willingham dove for a spectacular catch.
Hosmer was walked intentionally by McCarthy to load the bases with none out in the ninth inning just before Mike Aviles' game-ending sacrifice fly scored Jarrod Dyson.
"I was excited when the coach was going out there, that they were going to bring the lefty in," Hosmer said. "But they ended up sticking with McCarthy because they wanted the righty-righty matchup. With Mike at the plate and Dyson on third, you just knew the run was going to get in somehow."
His second day as the Royals' first baseman went a bit easier.
"It did, definitely," he said. "The last 48 hours have just seemed like a flash for me right now. It truly is unbelievable and tomorrow's going to be even easier. I got the first hit out of the way and I can just settle in now and go out and enjoy playing baseball."
Hosmer also got to enjoy his first walk-off celebration.
"That was awesome," he said. "It was the first one of the year for me and to get to do it on a big-league stage and in front of a packed house is unbelievable. It's my first big league victory and it couldn't have come in a sweeter way."
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.