Leicestershire 28 for 0 trail Glamorgan 403 for 9 dec (Neser 176*, Swepson 69) by 375 runs
The Australian all-rounder hit a career-best 176 not out and James Harris 47 as the pair put on 128 for the eighth wicket before Mitchell Swepson smashed 69 off just 70 deliveries – his best-ever score – as he and Neser added another 123 for the ninth wicket.
It was a remarkable recovery from the hosts after the Foxes had ripped through the Glamorgan top order to leave them teetering on 93 for 7 just after lunch.
Glamorgan eventually declared on 403 for 9 in their first innings in a match severely truncated by the weather.
A dispirited Leicestershire closed the day on 28 for 0 from seven overs in reply in their first innings to leave a draw odds-on on day four.
With just 17 overs possible in the first two days due to persistent rain in Cardiff, further showers meant a delayed start on day three.
Play got under way at 11.45am with Glamorgan restarting on 54 for 1 and eager to make up for lost time.
Zain ul Hassan resumed on 32 and Sam Northeast on 15. Eight balls later, however, the rain and the covers returned with just one run added to the overnight score.
Two balls after the resumption, Northeast was bowled by Chris Wright having not added to his overnight score.
Ul Hassan followed him back to the pavilion shortly afterwards when he was caught in the slips by Louis Kimber for 33 off the bowling of Matt Salisbury.
And Kiran Carlson was then bowled by Wright for 1 having faced only eight balls to leave the hosts on 57 for 4 and 3 for 3 from the first six overs of the morning.
It was left to Chris Cooke and Billy Root to try to rebuild the innings and Root signalled his intent with successive boundaries off Wright to finally get things moving for Glamorgan.
But Root’s revival didn’t last long as he was out for 12 having edged Tom Scriven to Kimber, who made an excellent catch at third slip to reduce the home side to 73 for 5.
That brought Neser to the crease and he and Cooke survived the Leicestershire onslaught to take Glamorgan to 86 for 5 at lunch.
But, having been dropped by Kimber in the final over of the morning session, Cooke was given out lbw to Scriven from the first ball after lunch for 10.
In the very next over, Timm van der Gugten drove Salisbury for four and was then promptly caught behind by wicketkeeper Peter Handscomb off the following ball to leave Glamorgan in trouble on 93 for 7.
When Harris was dropped on 10 by Colin Ackermann in the slips, it looked as if the innings would be wrapped up in no time and Leicestershire were eyeing an improbable victory.
But Harris and Neser made the most of that life to steer the home side to 218 for 7 at tea and almost certainly take a positive result out of the equation.
Harris was eventually out lbw to Scriven just after tea, but fellow Australian Swepson’s aggressive approach allowed Neser to complete his first home century for Glamorgan and earn his side an unlikely fourth batting bonus point.
Swepson reached his maiden first-class 50 with a smart pull for four and was finally stumped by Handscomb off the bowling of Callum Parkinson after attempting one big hit too many on 69.
Neser and No.11 Jamie McIlroy added another 59 before a weary Leicestershire were put out of their misery just after 6.20pm.
Day four is scheduled to get underway at 11am on Thursday.