After MCC captain Stuart Broad won the toss and opted to bat, McKerr struck early, bowling Dom Sibley and Tom Westley to put MCC in trouble at 45 for 2.
After van den Bergh had opener Will Rhodes (46) stumped by Jamie Smith, the 18-year-old Surrey wicketkeeper making his first-class debut, MCC were 107 for 3 but then Lawrence (58) and Tom Abell (41) steadied the innings.
When Abell was out lbw to Scott Borthwick, MCC's score looked much healthier at 193 for 4 but van den Bergh made the breakthrough when he had Lawrence caught behind by Smith and then had Peter Trego caught by McKerr a short time later.
County champions Surrey removed the potential danger of Dom Bess, dismissed by an excellent run out at the hands of Smith for four, and Broad, bowled by paceman McKerr, who finished the day with 3 for 40. Borthwick ended with 2 for 55, while fellow spinner van den Bergh had 3 for 54.
At the close of play, Surrey were 20 for none in reply, 245 runs in arrears, with England opener Rory Burns not out seven and Mark Stoneman unbeaten on eight in the four-day, first-class fixture.
Meanwhile, Lancashire won their one-day pre-season match against UAE in Dubai by six wickets with 38 balls remaining after reaching 233 for 4 in reply to UAE's 230 for 8.
Lancashire spinner Matt Parkinson underwent surgery in Dubai to repair a deep cut to his jaw after being struck in the face off his own bowling by Stoneman in the T10 Festival at the ICC Academy on Thursday. Parkinson, who did not suffer any fractures, was set to return to England early, while the rest of Lanchashire's squad head home later this week following a two-day fixture against UAE starting on Tuesday.