With 55 percent of the precincts counted, Lincoln had 44 percent of the vote to the Arkansas lieutenant governor's 42 percent. D.C. Morrison had 14 percent. The Arkansas Democrat Gazette said a runoff was inevitable.
On the Republican side, U.S. Rep. John Boozman was polling 52 percent to 16 percent for Jim Holt and 12 percent for Gilbert Baker. Five other GOP contenders had 6 percent or less.
If no candidate in an Arkansas primary gets 50 percent or more, there is a runoff.
Lincoln, who has the support of President Barack Obama and former President Bill Clinton, has had a target painted on her back by both Democrats and Republicans. Halter, backed by several powerful unions, has depicted her as a Washington insider and himself as a fresh force for change.
Republicans see Lincoln's seat as ripe for plucking in the fall. Real Clear Politics lists Lincoln's seat as "Likely Republican."
"It's a tough year. It's a crazy year," Lincoln said prior to the voting.
In Arkansas' 1st Congressional District, where Democratic incumbent Marion Berry is retiring after six terms, the Arkansas Democrat Gazette declared Rick Crawford, a regional agri-news network owner, the winner over political organizer Princella Smith in the GOP primary. Crawford had 70 percent of the vote to Smith's 30 percent with a quarter of the precincts counted.
On the Democratic side, former state Sen. Tim Wooldridge led with 36 percent to 29 percent for Berry Chief of Staff Chad Causey and 14 percent for state Rep. David Cook. Three other Democrats were polling 8 percent or less.
In the 2nd District, where Democratic incumbent Vic Snyder is retiring, the Democrat Gazette said Tim Griffin had bested Scott Wallace for the Republican nomination. Griffin had 61 percent of the vote to Wallace's 39 percent with 29 percent of the precincts counted.
On the Democratic side, state Sen. Joyce Elliott led with 37 percent to 32 percent for state House Speaker Robbie Wills. Four other candidates had 17 percent or less.
In the 3rd District race to fill Boozman's seat, Rogers Mayor Steve Womack led with 33 percent to 16 percent for state Sen. Cecile Bledsoe, 15 percent for former lawmaker Gunner DeLay and 11 percent for former lawman Bernie Skoch. For other candidates were in single digits.
Fayetteville City Attorney David Whitaker is the lone Democratic candidate for the seat.
In the 4th District Republican primary, Beth Anne Rankin, a former Miss Arkansas, had 55 percent to 45 percent for Tea Party activist Glenn Gallas with 51 percent of the vote counted.
Rep. Mike Ross is running unopposed on the Democratic side.