With 66 percent of precincts reporting early Wednesday morning, Barber won with 53 percent of the vote, the New York Times reported, compared to his Republican opponent, who had 45 percent of the vote. A Green Party candidate finished third, with 2.3 percent of the vote.
The race to win Giffords' former House seat in Tucson-based Congressional District 8 rose to national prominence in the aftermath of a shooting attack last year that Giffords survived.
Giffords was outside a Tucson Safeway supermarket at a meet-and greet with her constituents in January 2011 when a Tucson gunman went on a rampage and opened fire, leaving six people dead and more than 12 others injured, according to Politico.
The shooting and Giffords' miraculous survival made national headlines for months.
As a result of her injury, Giffords, who Reuters described as a former rising star in the Democratic Party, resigned her seat in Congress earlier this year to focus on her recovery.
The contest to fill her seat and finish her term pitted Barber, a 66-year-old former Giffords aide who was shot in the face and thigh during the 2011 shooting, and who was handpicked by Giffords to replace her, against Jesse Kelly, a 30-year-old Iraq War Marine veteran employed by his father's construction business, Reuters said.
This was Kelly's second attempt to represent his district in the House of Representatives after narrowly losing to Giffords in 2010.
At the time, Giffords was a three-term incumbent, and Kelly lost by only 4,000 votes, according to the New York Times.
Congressional District 8 is a border district in a border state, where Republicans outnumber Democrats, independent voters comprise a significant part of the electorate, and conservatives have historically dominated.
Giffords' shooting and stunning recovery garnered national attention, and as a result, national themes overtook the contest as it became a warm-up of sorts for the presidential election this November for both major national parties.
While Kelly and national Republicans tried to brand Barber as a rubber stamp for Barack Obama and the Democratic Party, Barber struck an independent tone, the New York Times said, so much so he wouldn't say whether or not he would vote for Obama this fall, or whether or not he would have voted for the president's health care bill.
According to Reuters, Republicans tried to tie Barber to Obama by claiming that Barber was a pawn of the president and Democratic leaders, and they used the Arizona special election to highlight criticism of Obama's signature heath care legislation and job creation efforts.
Firing back, Barber and Democrats claimed that Kelly wanted to do away with Medicare and Social Security, and they too used the election as a sounding board for the various themes and ideas they wanted to test out in preparation of this fall's presidential race.
The Democratic strategy won Tuesday night, but not by a great margin.