Former congresswoman Debbie Halvorson conceded after returns showed her lagging far behind, the Chicago Tribune reported.
"This is a big night for Robin, she did a great job," Halvorson said.
With nearly 69 percent of the 2nd District's precincts reporting, Kelly, a former state lawmaker, had 53.9 percent of the vote to 22.5 percent for Halvorson and 10.4 percent for Chicago Alderman Anthony Beale in the field of 14 candidates.
In the Republican primary, the Tribune said Paul McKinley held a slim lead over Eric Wallace 28.4 percent to 27.3 percent with Lenny McAllister in third place in the four-candidate field with 23.1 percent.
Tuesday's winners go on to the April 9 special general election. Kelly is widely expected to win the House seat.
Gun violence was a key issue in the largely black and heavily Democratic district that includes urban, suburban and rural voters.
Nearly half the district's voters live in the eastern part of Chicago's South Side, where some of the nation's most intense gun violence has occurred of late. The rest live in southern Cook County, eastern Will County and Kankakee County.
Most Democratic voters live in suburban Cook County, with an additional third from the South Side.
The region was pelted with snow, adding to election officials' predictions of a low voter turnout, which was in the teens, the Tribune said.
The race originally focused on ethics after Jackson became the latest of three district representatives -- preceded by Gus Savage and Mel Reynolds -- to leave congressional office amid scandal.
Jackson, the son of civil rights activist the Rev. Jesse Jackson, resigned in November, 15 days after winning re-election, citing health issues and acknowledging he was under federal investigation.
Before his resignation, he was on medical leave for treatment for "bipolar II depression" at the Mayo Clinic in Minnesota.
Jackson, who served nine terms in Congress, pleaded guilty in federal court Wednesday to using $750,000 in campaign money to finance a lavish personal lifestyle.
Savage was found guilty by the House Ethics Committee in January 1990 of fondling a Peace Corps volunteer the year before while on an official visit to Zaire. The committee decided against disciplinary action because Savage wrote to the woman saying he "never intended to offend" her.
Savage was re-elected in 1990 and ousted in the 1992 primary by Reynolds.
Reynolds was convicted in 1995 of having sexual intercourse with a 16-year-old campaign volunteer, as well as obstruction of justice.
He spent more than two years in prison before his sentence was commuted by President Bill Clinton in 2001 just before he left office. Reynolds was also in prison at the time for unrelated federal charges involving campaign and bank fraud.
But the campaign to replace Jackson quickly moved from ethics to gun violence after Connecticut's December Sandy Hook Elementary School shooting that killed 20 schoolchildren and six adult staffers.
Suddenly the Chicago-area district's own gun violence became the focus in one of the first big elections since the Newtown massacre.
New York Mayor Michael Bloomberg's Independence USA super political action committee announced Jan. 30 it would start "a significant TV ad campaign around educating Chicago voters about former Rep. Debbie Halvorson's abysmal gun safety record."
The Independence USA PAC, financed by Bloomberg, has spent more than $2.5 million to promote Kelly and attack Halvorson through TV ads and a direct-mail campaign.
It especially targeted Halvorson's "A" rating by the National Rifle Association.
Halvorson, who lost to Jackson in the 2012 primary, says she supports gun-purchase background checks and firearms registration but opposes an assault weapons ban.
Kelly has her own allegations of ethical impropriety. She was alleged by the state treasurer's chief investigator of violating ethics laws, after losing a 2010 bid for state treasurer, three years after she left the Illinois House.
The treasurer's executive inspector general alleged Kelly improperly reported time off from her taxpayer-funded job as Treasurer Alexi Giannoulias' chief of staff, the Chicago Tribune reported.
Giannoulias had announced a run for the U.S. Senate and Kelly ran to replace Giannoulias.
Executive Inspector General David Wells recommended Kelly be disciplined for the alleged timekeeping violations during her campaign, but no action was taken because she had already resigned from state government, the Tribune reported after reviewing records obtained under the Freedom of Information Act.
Kelly is now the Cook County chief administrative officer.
Kelly's campaign issued a statement after last week's Tribune report quoting Kelly as saying "any implication of misconduct is flat-out false" and saying she "was targeted by a politically motivated Republican witch hunt."