After resuming their innings on 282-6, Khaya Zondo was bowled by Sam Cook without adding to his overnight score of 86.
But 62 from Verreynne and 54* from Jansen got them well past 400, with Keshav Maharaj chipping in with 16 and Glenton Stuurman with 24.
At stumps, the England Lions were 279-3 after 55 overs, with Dan Lawrence (97), Harry Brook (64*) and Dom Sibley (48) making significant contributions.
Duanne Oliver was the Proteas’ most successful bowler, taking 2-39 in 10 overs.
The Proteas are giving 13 players game time in this match (11 batting, 11 fielding) ahead of the first Test against England at Lord’s, which starts next Wednesday.
