Daba covered the 26.2-mile course in 2 hours, 7 minutes, 4 seconds, breaking the record of 2:07.37 set by fellow Ethiopian Teshome Gelana last year. Gelana was unable to defend his title this year because visa problems.
American Nick Arciniaga was second (2:11.30) and Kenya-born Wilfred Murgor was third (2:11.41).
Mamitu Daska finished in 2:26.33 to become the fifth straight female champion from Ethiopia. Her time was nearly three minutes slower than Teyba Erkesso's record of 2:23.53 set in better conditions in 2010.
Sunday's race started under cloudy skies and light drizzle with a temperature of 64 degrees. The rain picked up by midmorning.
Pre-race favorite Brett Gotcher finished sixth (2:19.30) after posting the best time ever by an American in the event (2:10.36) in 2010.
Daba, Murgor, Gotcher and Kenyan John Kales were part of the early lead group that reached the 12-mile mark in just under 59 minutes.
Daba and Murgor separated from the pack between miles 16 and 17, building a lead of almost 30 seconds. Daba took the outright lead in the 18th mile as steady rain began to fall.
He maintained a brisk pace through the final five miles, and glanced at his wristwatch as he made the final turn. He lifted his right arm to acknowledge the cheering crowd near the finish line in front of the city's convention center.
Daba shaved seven minutes off his debut marathon in Amsterdam last year (2:14.39), where he finished 12th.
Erkesso, the two-time defending women's champion, did not enter this year.
Daska and top-seeded Ashu Kasim were among four Ethiopian women in a lead pack that reached the four-mile mark in just over 22 minutes. Male runner Genna Tufa, also from Ethiopia, stayed just ahead of the women's lead pack much of the way, setting the pace.
Kasim and Daska broke away around the 16th mile, and stayed virtually stride-for-stride until Daska pulled away in the final two miles.
Jeff Eggleston won Sunday's half-marathon in a time of 1:08.17. Colleen DeReuck won the women's half-marathon in 1:16.16.
The city's half-marathon was run separately from the U.S. Half-Marathon championships, which was held Saturday on the 8-mile loop course that will host next year's U.S. Olympic marathon trials.
Eggleston dropped out of Saturday's race after eight miles because of fatigue. He woke up at 6:30 a.m. Sunday and decided to try the city's half-marathon on an easier route, with fewer turns.
"I was feeling fine, I was here for another day," Eggleston said. "I wanted to come back and enjoy the course and take part in the event and have a more positive experience."