Following the ruling, election officials counted the additional ballots to add them to the some 85,000 votes already tabulated in the four-way 5th Congressional District race.
However, the additional counting won't decide the outcome because a recount is planned next week.
State law requires a recount because of Biggs' small margin over Jones. He led by nine votes after last month's primary.
Maricopa County Superior Court Judge Joshua Rogers ruled in a lawsuit filed by Jones that 18 uncounted ballots must be tallied because those voters cast provisional ballots at incorrect polling places during the Aug. 30 primary and were not told that their votes wouldn't be counted.
Before the counting of the 18 additional ballots, Biggs had 25,228 votes and Jones 25,219 while two other candidates -- Don Stapley and Justin Olson -- each about 17,000 votes.
Biggs now has 25,240 votes after picking up 12 Friday while Jones got five votes and now has a 25,224 total. The other vote among the 18 provisional ballots counted went to Stapley.
The GOP nominee in the heavily Republican district in southeastern Phoenix suburbs will almost certainly replace Republican Rep. Matt Salmon, who is retiring.
With the required additional counting, county officials now plan to canvass the primary election results Monday.
The state canvass is also set for Monday, after the county submits its official results. State officials then will seek court permission for a recount.
The recount itself could begin and finish by Friday.
While Jones' lawsuit argued that Maricopa County should have counted votes from at least 300 eligible voters who cast ballots that weren't counted for various reasons, an attorney for Biggs argued during a hearing that Jones was creating chaos and disruptions in an attempt to win the election.
Rogers rejected several of Jones' arguments but said the 18 voters were denied their right to vote by poll workers' failure to direct them to the correct precincts.
The judge said, "numerous voters who were either told by poll workers that their vote would count or, by silence, were misled to believe that their vote would count, were disenfranchised."
Joseph Kanefield, an attorney for Jones, sent a letter to Maricopa County Recorder Helen Purcell on Friday afternoon asking her count 136 provisional ballots that were cast in the wrong polling place.
He said it was "a matter of fundamental constitutional law" and "the right thing to do for the voters" in the county and district.
"Unfortunately, it now appears that Christine Jones is headed back to court to further delay the voters' will and attempt to find a way to erase her 16-vote deficit," Biggs campaign consultant Adam Deguire said in a statement. "I suppose after losing the election and then losing the lawsuit, she is now hoping that a `third time's a charm."'
Matt Roberts, a spokesman for the Arizona Secretary of State's Office, said either or both campaigns could go to court next week to contest the official results once the state approves the canvass.
"This court fight is just getting started," he predicted.