Rutherford even climbed into an upper-cut which deposited a short ball from Broad high over point and into the enclosure in front of the players' pavilion for six.
Soon afterwards, Broad hit the same batsman on the head with a sharp bouncer.
But it was first-change Woakes who made the breakthrough when Rutherford cut him into the hands of point.
Woakes was rewarded for a much-improved spell from his first-innings efforts, and Broad also put himself in the wickets column in the next over when he switched to a fuller length and bowled a static Carl Cachopa for a third-ball duck.
The more expensive Onions looked a more likely wicket-taker too than he had first time round, but no one could find a way past Latham or Neil Broom up to lunch.