With 60 percent of the precincts in Illinois' 2nd Congressional District counted, Kelly, a Democrat, had 78 percent of the vote to 15 percent for Republican Paul McKinley, the Chicago Tribune reported. Green Party candidate LeAlan Jones was third ahead of three independents who also appeared on the ballot.
"Yes, we've seen some tough times and some setbacks. I know for some of you, your faith in your leaders is a little shaken," Kelly said in prepared remarks.
"Through your support, you put your trust in me. I thank you for that and I promise that I'll never let you down."
"Watch us take on the NRA [National Rifle Association], the Tea Party and anyone else standing in the way of safety," her statement said.
Turnout was low -- about 8 percent as of 1:30 p.m. -- in the scandal-plagued district, the newspaper said.
Jackson, 48, is to be sentenced June 28 for illegally using at least $750,000 in campaign funds to buy, among other things, a Rolex watch, celebrity memorabilia, furs, a cruise and two stuffed elk heads. He pleaded guilty Feb. 20 in federal court to conspiracy to commit wire fraud, mail fraud and false statements.
Last summer, he took a leave of absence to deal with mental issues and in August he was diagnosed with bipolar disorder.
His wife, Sandi Jackson, a former Chicago alderman, pleaded guilty to separate charges of filing false tax returns. Her sentencing was set for July 1.