Finally, the Senate has broken the judicial-nomination logjam:

WASHINGTON—A divided U.S. Senate on Tuesday confirmed Washington lawyer Patricia Millett to serve on a powerful U.S. appeals court, the first Obama administration nominee to receive approval since Democrats last month made controversial changes to Senate rules.

The 56-38 vote showed partisan divisions remained deep after Democrats changed rules to eliminate filibusters on most nominations. Ms. Millett picked up two Republican supporters—Sens. Susan Collins of Maine and Lisa Murkowski of Alaska. No Democrats opposed her. Sen. Chris Coons (D., Del.) didn't vote because he was delayed in returning to Washington because of an East Coast storm.

The Senate separately advanced the nomination of Rep. Mel Watt (D., N.C.), the president's pick to head the Federal Housing Finance Agency, which controls the government-supported mortgage-finance companies Fannie Mae FNMA +6.00% and Freddie Mac. FMCC +5.65% Using the new filibuster rules, Democrats pushed through a series of procedural votes to set up Mr. Watt for a final Senate vote later this week, capping the effort with a 57-40 procedural vote.

The moves came after Republicans previously blocked votes on Mr. Watt, Ms. Millett and two other current White House nominees for the U.S. Court of Appeals for the District of Columbia Circuit.

The D.C. Circuit is considered one of the nation's most influential because it regularly considers lawsuits challenging major federal rules and regulations.