The Bruins (47-17) will begin the best-of-three finals Monday against Mississippi State, which eliminated Oregon State with a 4-1 win in the afternoon.
The Tar Heels (59-12) twice loaded the bases in the ninth against Berg but came away with only one run, with the game ending on Landon Lassiter's flyout to center.
Both starters went six innings, with the Bruins' Grant Watson (9-3) allowing four hits and Kent Emanuel (11-5) giving up five singles and striking out seven.
UCLA opened the CWS with 2-1 victories over LSU and North Carolina State. The Bruins, with eight total runs, matched 1976 Eastern Michigan for fewest by a team in the metal-bat era that won its first three CWS games.
The Bruins scored single runs in the second and sixth innings and made it 4-0 in the seventh on Valaika's double.
North Carolina threatened in the fourth and seventh innings but couldn't push across any runs until Berg, the National Stopper of the Year, came on to start the ninth.
Cody Stubbs and Sky Bolte singled, and Berg walked Michael Russell to load the bases. UCLA coach John Savage made a mound visit after Berg went 1-0 to Mike Zolk, whose groundout scored Stubbs.
Berg struck out Parks Jordan, and the bases were loaded again when he walked Chaz Frank. When Lassiter's fly landed in Brian Carroll's glove, the Bruins' dugout emptied in celebration.
UCLA has held its opponents to two runs or fewer in 31 of 64 games and is 30-1 in those games.
Watson followed strong starts by Adam Plutko and Nick Vander Tuig with one of his own to help send the Bruins to the finals for the second time, and first since they were swept by South Carolina in 2010.
The elimination of North Carolina means the Atlantic Coast Conference will go without a national title in baseball again. The last ACC team to win the championship was Wake Forest in 1955.
Emanuel, the ACC player of the year and third-round pick of the Houston Astros, came into the game scuffling in the NCAA tournament. He had a 11.40 ERA over his last five appearances and didn't make it out of the third inning in the Tar Heels' CWS opener against North Carolina State.
The junior left-hander was solid in his 112-pitch outing. One of the two runs against him was unearned.
UCLA opened the scoring when Cody Regis's two-out chopper drove in Gallagher in the second. The Bruins added their unearned run in the sixth. Eric Filia's grounder got past the glove of Carolina first baseman Stubbs, and he scored on Kevin Williams' base hit up the middle.
Valaika produced some big insurance runs in the seventh, hammering the ball into the left-field corner off Trevor Kelley to drive in Carroll and Filia.