Democrat Scott Colom Wednesday was on the brink of wrapping up a historic win in the Mississippi Senate race after he extended his lead by gaining ground in a new batch of votes.

Colom increased his edge over Republican incumbent Sen. Cindy Hyde-Smith to nearly 4,000 votes, or more than .3%, after he was expected to overwhelmingly win 817 approved provisional ballots from deep-blue Hinds County, which includes the city of Jackson.

Hinds County voters cast about 2,400 provisional ballots but officials rejected about two-thirds of them, a share that is much higher than in other Missis...