The Orioles didn't get another hit until Joseph singled leading off the eighth.
Each of Baltimore's last six games has been decided by one run, four of them in extra innings. The Orioles fell to 12-4 in extra innings.
Baltimore starter Bud Norris scattered eight hits over seven innings, striking out four and walking one. The right-hander is 5-0 with a 0.43 ERA in six career starts against Los Angeles.
The Angels loaded the bases in the third before Pujols grounded into a double play for the second time in two at-bats. He made up for it later.
Despite the loss, the AL East-leading Orioles won the season series 4-2. All six games were decided by two runs or fewer.
Skaggs walked the first batter he faced, and then retired 14 straight before walking Steve Pearce in the fifth. The lefty threw one more pitch before leaving.
Angels: Left-hander C.J. Wilson, who has been sidelined since July 10 with a sprained right ankle, is expected to return Saturday to start at Tampa Bay.
Orioles: First baseman Chris Davis (stomach virus) missed a third straight start but entered as the designated hitter in the ninth. He struck out and walked. Left-hander T.J. McFarland returned from bereavement leave and righty Preston Guilmet was optioned to Triple-A Norfolk.
Angels: Matt Shoemaker, who went 3-1 in July, seeks to extend that run into a new month Friday night in the opener of a three-game series in Tampa Bay.