Jermaine Beckford’s late goal spared Leeds United from going out of the FA Cup to non-league opposition for the second successive season.
Beckford diverted Robert Snodgrass’s low cross past Kettering keeper Lee Harper to earn a second-round replay.
Poppies took the lead through Ian Roper, who headed Richie Partridge’s free-kick into the net via the bar.
Earlier, Harper tipped Jason Crowe’s header over the bar while Simon Heslop had his shot saved by Casper Ankergren.
Both teams will have a strong incentive in the replay after the third round draw set up a trip to Manchester United for the winners.