Leicestershire's Stuart Broad turned in a superb display in front of England chairman of selectors David Graveney, but Surrey took control of the match.
Broad took career best figures of 5-94 to help bowl Surrey out for 370, but the visitors were well on top as Leicestershire finished 244 all out.
John Maunders made 87 to top the scoring for Leicestershire, while Darren Maddy made a quickfire 43.
Tim Murtagh and Nayan Doshi (3-21) were the pick of Surrey's bowling attack.
Broad, who also shared an eighth-wicket stand of 56 with Maunders, is the son of former England opening batsman Chris and has been tipped as one of England's brightest young bowling prospects.
With two wickets to his name from day one, Broad started day two in top form, taking Mark Butcher's off stump out of the ground in his second over.
Surrey then lost six wickets falling for 35 runs in eight overs as Broad and his fellow bowlers got the most out of the conditions.
But Leicestershire's batsmen struggled against Surrey's seamers, losing five wickets for 88 runs in 29 overs.
Murtagh dismissed Dinesh Mongia, HD Ackerman and Jeremy Snape, while Maddy went to Azhar Mahmood.
Leicestershire were struggling to make the follow-on target at 173-7, but Broad and Maunders' stand helped them move past it.