Durham 217 (Wood 72, Weighell 55, Claydon 5-54) and 359 for 7 (Latham 119, Clark 86, Haggett 3-82) drew with Kent 206 (Northeast 110, Onions 6-62) and 184 for 9 (Billings 70*, Northeast 67, Weighell 3-51)
Kent's Sam Billings returned from the migraine which had laid him low for two days to defy Durham, and their record-breaker Graham Onions, in the Specsavers County Championship match at Chester-le-Street.
Set a more than challenging target of 371 in 56 overs, there were 28 overs left when Billings went in at 74 for 5. But while four more wickets fell he remained unbeaten on 70.
There were six overs left when Onions pinned Adam Milne lbw to break the record of 518 first-class wickets for Durham, held since 2002 by left-arm seamer Simon Brown.
That brought in Imran Qayyum, but he was well protected by Billings and faced only two balls before edging the first ball of the penultimate over to Paul Collingwood at first slip off James Weighell.
Last man Mitch Claydon, who defied his old teammates when Kent also hung on with nine wickets down at Canterbury, survived the over and Billings then kept out Onions.
Kent closed on 184 for 9, leaving Durham to rue their belated declaration and accept their frustrating fate in a match which lost four sessions to the weather.
Kent skipper Sam Northeast followed his 110 out of 206 in the first innings by making 67 of the first 112 runs. He was sixth out, inside-edging a drive at Keaton Jennings into his stumps, with 15.2 overs left.
Kent coach Matt Walker said: "We were surprised they batted on after lunch. We thought 300 was enough on a pitch which had enough in it for a quality bowling attack. I thought they would have wanted 65 overs, but it nearly worked for them.
"With Worcestershire winning we would have liked to have a crack at a target, but 370 was too many.
"In terms of the situation and the way he has been feeling for the last two days that's as well as I've seen Sam Billings play in four-day cricket. He didn't feel right after day one and still wasn't 100 per cent today, but he showed great character and skill. To see us home was an excellent effort."
Durham coach Jon Lewis said: "We played a lot of good cricket in the match and we're on a good unbeaten run, so we didn't want to give them a chance.
"When you have a side nine down questions are always asked about the declaration, but the outstanding first spells by Onions and Rushworth probably worked against us. We were hoping Kent would feel under pressure to go for it, but it knocked the stuffing out of them."
After passing 1,000 championship runs in the morning, Paul Collingwood batted on for 7.3 overs to add 62 after lunch before declaring on 359 for seven.
Following Worcestershire's win the belief was that Kent would have to go for it to retain any hope of promotion. But it was out of the question once they lost both openers without a run on the board.
Onions struck with his first ball, having Sean Dickson caught behind and in the next over Daniel Bell-Drummond went the same way to Chris Rushworth.
On ten, Northeast edged Rushworth past Collingwood's left ear at first slip and had progressed to a 69-ball half-century by the time Billings joined him and played a few shots of his own. The wicketkeeper hit ten fours in his 72-ball half-century.
In the morning Tom Latham completed his second century in three games for Durham. He survived a sliced drive to Joe Denly at gully off the luckless Milne on 65 and was becalmed in the 90s, tied down by Claydon, before a back-foot four through the covers took him to his hundred off 221 balls.
After resuming on 49, Graham Clark progressed solidly to 86 before skying an attempted pull off Claydon to end a stand of 180 and bring in Collingwood, who got off the mark by driving left-arm spinner Imran Qayyum over long-off for six.
On 20 he lifted the same bowler to the mid-wicket boundary to reach the 1,000 target, but was bowled for 35 when he went down the pitch to Qayyum.
In the post-lunch thrash Latham departed for 119 when he was caught one-handed above his head by the 6ft 6in Zak Crawley at extra cover. Ryan Pringle hit an unbeaten 30 off 23 balls and the declaration came when Mark Wood was bowled by Denly for 24.
When Wood had Crawley caught behind with the second ball after tea he looked a possible match-winner. But in his comeback match after a six-week absence with the latest of many injuries he left the field shortly afterwards.