Leicestershire 422 (Ackermann 146, Mulder 56, Raine 4-114) and 259 for 8 (Handscomb 136*, Raine 4-55) drew with Durham 517 for 6 dec and 343 for 4 dec (Lees 145, Bedingham 145)
The Australian wicketkeeper-batter finished on 136 not out, his second hundred for the county, before bad light ultimately had the final word with Leicestershire 259 for 8 with 10 overs left in the match.
Durham will feel that they were denied by the elements, but Leicestershire had battled through 20 overs at eight down, largely against spinners Matt Parkinson and Liam Trevaskis with fielders crowded round the bat, but Handscomb managing the strike so well that ninth-wicket partner Ed Barnes faced only 43 balls in 71 minutes at the crease.
Earlier, Durham had declared at 343 for 4 after Alex Lees (145) and David Bedingham (145 not out) had shared a 243-run stand for the third wicket, giving themselves 89 overs to take 10 wickets and Leicestershire a theoretical 439 to win.
Ben Raine finished with 4 for 55, including two wickets in his first four deliveries with Matthew Potts and Parkinson collecting two each. Their efforts were ultimately in vain but the 13 points they took from the match stretches their lead to 36 ahead.
Durham's requirements for the run chase were met after 47 were added in 28 balls to the overnight total before the declaration came.
Lees could add only seven to his 138 not out before he was caught in the deep slog-sweeping Callum Parkinson, who also bowled his fellow slow left-armer Liam Trevaskis for seven. Bedingham was the biggest contributor in this entertaining burst of slogging, plundering 33 from 16 balls.
Some Durham supporters grumbled that batting on had used up valuable bowling time but this pitch had yielded runs at more than 4.5 per over in the opening three days and skipper Scott Borthwick would have been mindful of Leicestershire chasing down 389 to win at 4.56 per over to beat Yorkshire at Headingley in April.
In the event, the possibility of a Leicestershire win receded almost immediately as Raine had Sol Budinger caught behind swinging at one he perhaps should have left and Hill edging to first slip first ball, which he did need to play. Rishi Patel had been dropped at short midwicket off Raine's first delivery.
By the seventh over, Leicestershire were 23 for 3, Patel having picked up two boundaries in the over off Raine before he was caught at deep backward square off a top-edged hook as he went for another.
Handscomb and Colin Ackermann added 61 without further loss before lunch, although the latter had enjoyed a slice of luck 31 when Bedingham put down an edge to second slip, again off Raine.
Potts dismissed Ackermann soon after lunch, Leicestershire's first-innings centurion driving loosely away from his body to nick one through to Ollie Robinson off an inside edge.
Much now rested Handscomb, who reached his half-century from 73 balls, and the South African Wiaan Mulder to keep Durham's bowlers away from a lengthy tail.
Their cause was helped by a stoppage for bad light and light rain, taking eight overs out of the game, but set back again when they returned after an early tea to lose Mulder caught behind - a decision with which he plainly disagreed - and new man Tom Scriven caught at second slip in consecutive overs as Raine took his fourth wicket and Potts, despite needing treatment on the field for an apparent neck problem, his second.
After Matt Parkinson entered the attack to dismiss Chris Wright, caught at slip, with his fourth ball, Leicestershire were 181 for 7. It should have been 187 for 8 in the leg-spinner's next over, but Callum Parkinson survived a chance to short leg.
It was only a brief reprieve, however, Callum judged leg before on the front foot in his brother's next over. He had been dismissed by Matt in that way in the twins' only previous first-class meeting, at Grace Road in 2019, in which by coincidence Callum also trapped Matt leg before.
With 26 overs still left, Leicestershire were now desperate for the weather to intervene but as that threat receded it was down to Handscomb to protect his two remaining partners.
The Australian picked off boundaries with relative ease as he completed his second hundred for the county with his 14th, although he had an escape on 110 when a leading edge off Liam Trevaskis looped just beyond the reach of Borthwick at short mid-on and survived a confident appeal for caught behind just before the light closed in for the last time.