Borthwick claimed his first wicket in his fourth over, when Rajapaksha (36) skied the ball to Muchall at backward point, with Sri Lanka A having established a lead of 38.
Breese struck when Rajapaksa (6) was caught by Wood with the visitors 155-4 and 40 minutes of play remaining in the day.
Play was brought to an early close due to bad light but the allocated numbers of overs had been bowled. At the close Sri Lanka A were 184-4 with a lead of 84.