The Royals trailed 5-0 after two innings and 8-3 going into the sixth when Ankiel hit a three-run homer. Ankiel also singled home David DeJesus in the fourth.
"I think that's the biggest thing out in Arizona, it is light air and no lead is safe," Ankiel said.
He said he did not think his home run to right-center was out.
"I didn't think I got extended enough on it, but fortunately I did," he said.
Wind gusts of up to 33 mph played a factor offensively and defensively.
"It was a lot harder to play defense," Ankiel said. "The wind was blowing pretty hard out there to the point it made your eyes water. I've heard before if you can play this (Arizona) outfield, you can play anywhere, so I guess it's a good starting point."
Jack Cust hit a two-run homer to right in the first that bounced out of the stadium.
"The first one is always a little weird," Cust said. "You usually don't know if it's out, but that one I hit right down the line and I knew it was out. You don't look at it the whole time, but you kind of see the trajectory. Sometimes you hit your best balls when it's windy when you don't need the help. It's kind of weird trotting around the bases again for the first time. It seems like it's kind of long."
Cust also doubled in a run in the fifth and scored on a Landon Powell double. Corey Brown, who replaced Travis Buck in the lineup, had three hits, walked, drove in two runs and scored twice. Buck was a late scratch with dizziness.
A's starter Vin Mazzaro was sharp, allowing one hit and facing the minimum number of batters in three innings. He gave up a leadoff single to Scott Podsednik, but picked him off. He walked Billy Butler to leadoff the third, but Jose Guillen grounded into an inning ending double play.
Robinson Tejeda, who is a candidate for a Royals rotation spot, gave up five runs on four hits, three walks and a wild pitch in two innings.
"I don't say it was too many walks." Tejeda said. "This is nothing new for me. I've been walking people for my whole career. I'm not going to let this get on me. I'll just try to think positive and next time try not to walk anybody, be more consistent in the strike zone and try to make all my pitches and try to look good."
Kyle Davies, another rotation candidate, replaced Tejeda and allowed three runs on five hits and two walks in three walks.
"I'm concerned. I'm not frustrated," Royals manager Trey Hillman said of his pitching. "It's not a lot of fun watching major league pitchers or guys trying to make the club not command the fastball."
Vance Wilson's wild blown infield single with two out in the ninth scored David Lough, who had a run-producing triple, with the winning run.