Earlier Robson survived after offering a tough chance to short midwicket from the second ball of the day, running a single to bring up his half-century.
He played a silky cover drive off Conway to mark the century partnership with Holden who reached his own 50 by pulling Sanderson behind square.
The pair saw off the initial burst from Sanderson and Conway and found it increasingly easy to score against the aging ball, 102 runs coming in the morning session. Robson moved through the eighties as leant into a glorious cover drive off Liam Guthrie and drove Harrison through the covers.
Holden though departed when he tried to pull one from Harrison which turned sharply and kept low.
Northamptonshire rotated their spinners after lunch, ensuring they moved ahead of the over rate, Robson driving Nathan McSweeney through cover before running a single to bring up his century.
Du Plooy showed positive intent, cutting and sweeping to take Middlesex past 250. He reached his second half century of the match by pulling a drag down from Harrison, before driving Saif Zaib through mid-off.
Northamptonshire delayed taking the new ball until the 94th over, opting to bowl Guthrie and Sales in order to manage the workload of their frontline seamers.
Robson cut Guthrie through backward point and then drove him through cover to go past 150 before a leg glance off Guthrie brought up Middlesex’s 350. Next ball though Robson departed when keeper Lewis McManus pulled off a stunning one-handed flying catch down the legside.
Middlesex went into tea having added 141 in 37 overs in the afternoon session but just one over was possible after the interval before the umpires took the players off.
