Huff (2-2) allowed three hits and two walks while striking out four to earn the win.
"He was aggressive in the zone with his fastball and his cutter, especially against the right-handers," said Indians manager Manny Acta.
Chris Perez tossed a perfect ninth to record his 30th save of the season.
Santana and Fukudome both had a pair of hits for the Indians, who have won three of four. They now sit in third place in the AL Central, a half game behind the second-place White Sox and 5 1/2 games behind the first-place Tigers.
Brandon McCarthy (7-7) gave up two runs on five hits over eight innings to suffer just his second loss since July 4. He walked one and registered a career-high 10 strikeouts.
"He pitched great," A's manager Bob Melvin said of McCarthy. "He gave up really, the one pitch, which was the home run."
Jemile Weeks had an RBI double for the A's, losers of three in a row and four of their last five.
Tonight, Jeanmar Gomez will be recalled from the minors to get the start in place of the injured Josh Tomlin. Gomez has pitched in five games (four starts) for the Tribe this season and is 0-2 with a 5.70 ERA.
Getting the call for the A's tonight will be righty Trevor Cahill, who is 9-12 with a 4.13 ERA and hasn't won since beating Tampa back on July 27. Cahill, though, pitched well his last time out on Wednesday in New York, as he held the Yankees to a pair of runs and seven hits in six innings. However, he did not get a decision in his team's 6-4 win.
Cahill gave up a run in seven innings to beat Cleveland earlier in the year and is 2-1 with a 3.06 ERA in three starts.
Cleveland took two of three from the A's earlier in the year.