Only 21 balls were possible in a rain-hit morning session at New Road.
After Australian paceman Jackson Bird had taken his third wicket, the hosts then looked in some discomfort at 25-3.
But Mitchell put on 142 with teenager Joe Clarke (70), finishing the day on 105 as Worcestershire closed on 228-5.
Worcestershire got off to a bad start when Richard Oliver, their T20 matchwinner against Durham the day before, was out to only the fourth delivery he received, leg before wicket to Bird.
After an early lunch following the mid-morning downpour, Tom Fell then edged Bird low to wicketkeeper Adam Wheater before the recalled Tom Kohler-Cadmore was bowled without playing a shot.
But the meeting of last season's two promotion winners then changed course as Clarke joined Mitchell, who made an unbeaten 142 at Southampton in May, only for Hampshire to be saved by the weather.
Kohler-Cadmore came in for his third Championship start of the summer as Alex Gidman was still feeling the effects of a blow he took on the helmet on the first day against Nottinghamshire a week ago.
The home side also opted to play an extra spinner, in-form T20 specialist Brett D'Oliveira coming in for seamer Ed Barnard.
Worcestershire skipper Daryl Mitchell told BBC Hereford & Worcester:
"It's always pleasing to get a hundred and when we were 25-3, it's doubly pleasing to get us out of a bit of trouble. We will see how important it is at the end of the game.
"It's a good wicket, pretty dry and not a lot of grass, and I thought batting first was important with two spinners in the team.
"There was a bit of cloud cover and it did nibble around a little we overcame that and Joe Clarke played a fantastic innings."
Hampshire coach Dale Benkenstein told BBC Solent:
"It was a solid day but, at 25-3, there was a real opportunity and we got a little bit excited. We have not had those opportunities, especially recently.
"It's a fairly good, slow, placid wicket. We almost tried to get wickets but they got a bit away from us.
"If you bowl in good areas there is enough in the wicket and it's hard to score."
Worcestershire captain Daryl Mitchell compiled his second hundred of the season against Hampshire to help rescue his side against their fellow County Championship Division One strugglers.