Roberts had 51.2 percent of the vote, compared to 48.8 percent for Gaspar, the Encinitas mayor.
Roberts survived a scandal over the way he managed his staff to make the runoff election with Gaspar. Last year, the Board of Supervisors agreed to pay $310,000 to settle claims brought by three former staffers who accused Roberts of misusing his powers.
Four years ago, he became the first Democrat to win a seat on the board in a couple of decades. Gaspar is the chief financial officer and business manager for Doctors of Physical Therapy, which has six North County offices.
"I think the voters responded positively to my message of service over the last four years," Roberts told City News Service.
In another close race, Ricardo Flores took an early but relatively narrow lead in his bid to succeed his boss, Marti Emerald, in the San Diego City Council District 9 race. Flores led Georgette Gomez, 52 percent to 48 percent.
Flores is the chief of staff for Emerald, who opted to not run for re- election. Gomez is a longtime community organizer and activist with the Environmental Health Coalition.
Barbara Bry, the founder of ProFlowers.com, will succeed council President Sherri Lightner. Her opponent for District 1 -- representing Carmel Valley, La Jolla and University City -- Ray Ellis, previously dropped out of the race, but his name was still on the ballot.
Chief Deputy City Attorney Mara Elliott defeated Robert Hickey, a deputy district attorney, in a battle to succeed San Diego City Attorney Jan Goldsmith.
"I think voters liked the message that I was bringing to them -- to all neighborhoods for nearly two years -- which is that I want our office to be accountable," Elliott said. "I see us as protecting San Diegans, whether it's from elder abuse, child abuse or pollution."
She said the city attorney wears multiple hats -- including prosecuting misdemeanor crimes and providing legal advice to the mayor and City Council -- but is ultimately accountable to the taxpayers.
On the San Diego Unified School District Board of Education, Trustees Richard Barrera, John Lee Evans and Sharon Whitehurst-Payne all won re- election.