Steve Birnbaum anchored Cal’s defense last season, but also tied for second in the Pacific-12 in goals with 10. (Matt Rourke/Associated Press)

In the moments before the MLS draft commenced Thursday, D.C. United officials shuttled between their table and three outposts spread throughout the Philadelphia Convention Center’s ballroom.

United owned the first pick but probably didn’t need it to claim its most coveted player, California defender Steve Birnbaum.

Philadelphia, Dallas and Vancouver wanted Connecticut goalkeeper Andre Blake. So United fielded offers, confident it could swap places high in the first round, still claim Birnbaum and collect something else.

Philadelphia made the best pitch: the No. 2 pick and allocation funds, which can be applied toward future player acquisitions without impacting the salary cap. The Union proceeded to select Blake. United pocketed the allocation cash and took Birnbaum, a 6-foot-2 center back who anchored Cal’s run to the NCAA quarterfinals.

“It became a little bit of a bidding war in the last five minutes,” General Manager Dave Kasper said. Half-joking, he added that United finalized the trade at 11:59 a.m., a minute before the festivities began.

“It’s a win-win,” United Coach Ben Olsen said. “Philly got one heck of a goalkeeper, and we got our man. . . . Steve was the guy we had our eye on for months.”

Birnbaum becomes the fourth central defender acquired by United this winter, joining MLS veterans Bobby Boswell and Jeff Parke as well as Nana Attakora. With Boswell and Parke in their thirties, United believes Birnbaum will compete for a starting role in the near future.

“I’m excited to learn from them,” Birnbaum said of Boswell and Parke, “and take things from their game and incorporate it into mine.”

Among a deep group of center backs in the draft, Birnbaum was regarded as most prepared to play right away. Cal conceded 21 goals in 21 matches, the second fewest in the Pacific-12. And despite being a defender, Birnbaum was tied for second in the conference in goals with 10, most coming on headers off of corner kicks and free kicks.

“He has got all the tools,” Kasper said. “He is dominant in the air. With the ball, he rarely makes a bad decision. He’s a leader and has great positional sense. When you add all of that up, it was pretty clear he was going to be that guy.”

Last month, as part of its back-line makeover, United also acquired Sean Franklin, an experienced right back. The club remains in the market for a left back. United added a pair of proven forwards as well in Eddie Johnson (Seattle) and Fabian Espindola (New York).

“It was a priority for us to shore up the back line and add to the attack,” said Kasper, whose club won the fewest games in MLS history last year (3-24-7). “You add pieces at both ends of the field like that, and we are a much better team.”

United began the day without a second-round pick but traded an international roster slot to the Montreal Impact for the 29th overall selection. D.C. claimed UCLA midfielder Victor Munoz, a native of Spain who played in the Real Madrid and Celta de Vigo youth systems. He is left-footed and adept in the middle and on the wings.

The biggest surprise of the day was Maryland forward Patrick Mullins, the two-time Hermann Trophy winner who fell to the New England Revolution at No. 11. Mullins was projected to go in the top six, possibly No. 1, but questions lingered about his best position on the pro level and many clubs chose to address defensive needs.

United was quite familiar with the Terrapins star but felt it needed more defensive help.

“Surprised? No. Anything can happen,” Mullins said of his draft position. “I’m glad I ended up in a great place. I wanted to go to the best fit, and I think New England is the best fit for me.”

He will join Georgetown midfielder-forward Steve Neumann, New England’s selection with the fourth pick. Having played 11 miles apart for four years, Neumann and Mullins got to know each one another well and collided in the 2012 College Cup semifinals (won by Georgetown on penalty kicks). They roomed together at the scouting combine in Florida last week.

Maryland sophomore forward Schillo Tshuma, an Episcopal High graduate and The Post’s All-Met Player of the Year in fall 2011, was chosen by the Portland Timbers with the No. 17 pick.