Former Los Angeles city Controller Wendy Greuel, a Democrat, who placed third and thus cannot advance to the fall general election, did well in the Los Angeles Westside communities, winning the most votes in Bel-Air, Brentwood, Hollywood Hills West and Beverly Hills.
But radio host Matt Miller, also a Democrat, cut into Greuel's support, reducing her chances of securing the first-or second-place finish needed to compete in the Nov. 4 general election.
Miller, who finished fifth, won the most votes in Pacific Palisades, where he has lived for nearly two decades.
Placing fourth was spiritual teacher and best-selling author Marianne Williamson. She received her strongest support in Malibu and Venice, the Times analysis found.
Carr, a Republican and gang prosecutor who finished first among the 18 candidates on Tuesday's ballot, garnered a plurality of the votes from incorporated communities on the Palos Verdes Peninsula.
Lieu, a Democratic state senator, was the top vote getter in Torrance, his home base and the South Bay's largest city.
Carr and Lieu are now set to compete for the Westside votes that went to Greuel, Williamson, Miller and the rest of the field.
Waxman, a liberal icon in Washington and on the Westside, served for four decades in Congress and had a leading role in landmark legislation on environmental, healthcare and consumer issues.
His surprise Jan. 30 announcement he would not seek reelection drew the largest field of any contest on the state primary ballot.