Matsui's solo blast gives him a combined 499 homers in Japan and the U.S. and helped Oakland win a second straight game for the first time since a four-game streak May 26-29.
Gonzalez allowed two runs on five hits over six innings. He walked two and struck out 10.
Jeff Francis (3-7) gave up a season-high six runs on nine hits over 3 1-3 innings, his second- shortest outing of the season. He walked two and did not strike out a batter in a game for the first time.
A's interim manager Bob Melvin earned his first ejection in an Oakland uniform, getting tossed by third base umpire Tim Tschida in the top of the third.
Weeks' two-out double scored two runners in the second during the A's four-run rally. The rookie infielder is hitting .344 (11 for 32) since his June 7 call-up.
Matsui led off the third with his sixth home run of the season and third in seven games after going homerless in his previous 23 games. Barton later added his second RBI of the game.
The Royals scored twice in the fifth to make it 6-2 on Cabrera's single and Francoeur's double.
Weeks singled home a run in the bottom of the fifth and Suzuki doubled home a run in the seventh.
Betemit and Pena each doubled in a run for the Royals in the eighth.
Notes: Francis has not won consecutive road starts since 2007. He has a 6.93 ERA away from Kansas City. ... Barton tied Sean Casey for most games to start a season without a home run by a first baseman at 63. ... Melvin plans to give Matsui a start in each of the series played in National League parks during interleague play. ... Cabrera has a hit in 12 of his past 14 games. ... Francoeur went 1 for 5 and is now 2 for 20 with seven strikeouts on the road trip. ... A's right fielder Conor Jackson had a hit and walked against Francis, improving to .436 (17 for 39) against the left-hander.