Left-handed Mongai hit an unbeaten 90 while Manhas scored 97.
Earlier, skipper Virender Sehwag won the toss and elected to bat. North Zone made a poor start losing Test opener Gautam Gambhir cheaply. Left-arm seamer Rudra Pratap Singh bowled a probing spell, first accounting for Gambhir for two before dislodging Yuvraj Singh for six.
Skipper Virender Sehwag held the innings together to score a fine half-century but his departure for 51 saw North slipping to 73 for four. The stage was set for the duo of Mongia and Minhas play the saviour roles and they did it with perfection.
They raised 190 runs for the fifth wicket.
R P Singh was the pick of the Central Zone bowlers picking up four for 56.