Resuming on 86, Mitchell reached his 23rd first-class hundred, his first in 13 months, when he luckily edged Ben Sanderson to the third-man boundary.
After a four-hour rain delay, debutant Chad Barrett took a first Championship wicket, England Lions' Joe Clarke.
Bad light caused an abandonment with the hosts on 195-3, still 356 behind.
Worcestershire captain Mitchell, who had previously managed a first-class season's best of only 66, had enjoyed a chanceless innings until, on 98, Sanderson found his edge.
But the ball went to Rory Kleinveldt's left hand, where it was spilled before reaching the boundary to bring up Mitchell's century.
The 32-year-old shared a 152-run second-wicket stand with Tom Fell, who was brilliantly caught behind by a diving David Murphy off Sanderson.
The players went off soon after as the rain began to fall but, although just four overs were bowled after the resumption, it was enough time for Barrett's welcome scalp when Clarke played at a ball outside his off stump.
Worcestershire skipper Daryl Mitchell told BBC Hereford & Worcester:
"It is nice to contribute a major innings in red-ball cricket. Obviously I haven't got the runs I would have liked so to get over that line means a lot to me.
"The season has been a bit stop start for me. Three or four 50s and quite a lot of 30s and 40s, a lot of starts. I've found various ways to get out, caught in the ring and run-outs and things like that.
"Eventually it has to turn, and I've kept working hard. I got my rewards and had a bit of luck. I gave them a chance of getting me out but fortunately it went through the slip cordon for four."
Northants skipper Alex Wakely told BBC Radio Northampton:
"It has been a really frustrating day. The weather conditions were actually very good for bowling.
"Unfortunately we didn't get long enough in one go. Ben Sanderson again was outstanding, put the ball in the right areas and was making it talk.
"But Chad Barrett also ran in hard for us and got a few balls around the batsmen's head."
Daryl Mitchell completed an unbeaten century, but persistent rain saw only 17.2 overs bowled on day three between Worcestershire and Northants.