Joe Root, leading the Lions for the first time, chose to bowl on a pitch with plenty of green about it.
But Rutherford (66no) responded with 11 fours in his 55-ball 50 as the tourists reached lunch on day one of four on 102 for two.
There was little evidence of lateral movement off the pitch or in the air for the Lions seamers, and after two early plays and misses from Rutherford at Chris Woakes, the left-hander was soon climbing into a succession of off-side fours off either foot.
Rutherford's opening partner Peter Fulton lasted only until the seventh over before Graham Onions had him lbw aiming to his favoured leg-side.
Woakes dropped Kane Williamson at gully off Onions but the number three was soon gone anyway when he pulled a short ball in first-change Toby Roland-Jones' first over straight to midwicket.
Rutherford cashed in with three successive off-side fours off Roland-Jones when the Middlesex seamer was off target with both line and length, and reached his 50 with another back-foot boundary past cover off Chris Wright.
Ross Taylor was in less adventurous mood but appeared untroubled too by the Lions' frontline attack in an unbroken stand of 61, and Root turned to Ravi Bopara for three tidy overs before lunch.