Giellis (GILL-lis), an urban planning consultant in her first campaign for public office, said she congratulated Hancock in a telephone call. She vowed to continue "to fight for this city."
"We changed the conversation in Denver and we should be very proud of that," Giellis told her supporters.
Unofficial returns showed Hancock holding a 56%-to-44% lead as vote-counting continued.
"Are you ready for four more years?" Hancock asked cheering supporters at a watch party. Two former mayors — John Hickenlooper, who's seeking the Democratic presidential nomination, and Wellington Webb — stood smiling behind the beaming mayor.
Hancock insisted Giellis lacked the experience needed to steer growth in a city that's added nearly 100,000 jobs since he was elected in 2011.
Hancock touted his credentials as a former president of the Urban League of Metro Denver and city councilman, and his deep ties with Hispanic, African-American and Asian communities as key to promoting development while tackling affordable housing, homelessness and gentrification of historic neighborhoods.
Giellis, an Iowa native who's lived in Denver for 13 years, has been heavily involved in the transformation of an old industrial district north of downtown into a thriving community of arts, retail, residential and commercial enterprises.
She said she's seen growing worries among minorities and longtime residents at risk of displacement by gentrification, rising housing prices and big-box residential and commercial development. She's called for satellite offices putting city officials directly into neighborhoods.
"People are done with the old guard," Giellis said. "Denver grew up fast, and you still have a power structure that's trying to hold onto the old ways."
Since 2010, Denver's population has grown from 600,000 to 710,000. Energy, financial, tech and services firms have invested heavily. But U.S. Census data suggest 12% of residents live at or under the federal poverty level, defined as nearly $26,000 for a family of four.
In the campaign's final weeks, the candidates engaged in finger-pointing over sexually suggestive texts sent by the mayor and perceived racial insensitivity by his challenger.
Giellis criticized Hancock for suggestive text messages he sent in 2012 to a female police detective who served on his security detail. But he insisted in a recent debate that his actions didn't rise to the level of sexual harassment "because you don't see the back and forth conversation that occurred."
Hancock later apologized for that comment.
His campaign released video of Giellis, who is white, unable to state what the National Association for the Advancement of Colored People acronym stood for.
It also cited an old Giellis text, since deleted, questioning the need for cities to have Chinatowns. It also made an unfounded claim that Giellis called immigrants living in the country illegally "criminals."
Hancock, who is black, has defended those immigrants and limited local cooperation with federal immigration agents to that required by law. The Colorado Immigrant Rights Coalition says Giellis shares those views.
"I have a lot to learn in this process," Giellis acknowledged, vowing to work with, and learn from, communities of color she insists are most vulnerable to rising housing prices.