Laxman (63) hit five fours on the way to his 41st Test half-century while Yuvraj cracked four boundaries and two sixes in his 67-run knock to enthrall a strong 25,000 crowd at the Green Park stadium.
The pair also shared 102 runs for the fifth wicket before Laxman was caught by Tillakaratne Dilshan off left-arm spinner Rangana Herath (5-121).
Herath struck again twice, bowling Indian captain Mahendra Singh Dhoni and Harbhajan Singh through the gate to bring some cheer to the Sri Lankan camp in the post-lunch session.
Laxman and the left-handed Yuvraj dominated the second session, mixing caution with aggression in right measure.
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Yuvraj got down on his knees to launch Muttiah Muralitharan for a huge six over long-on before smacking Ajantha Mendis for two fours in an over, underlining India's dominance over the spinners on the placid track.
Laxman survived a strong appeal for leg before wicket off Herath although TV replays showed the ball would have clipped his leg-stump.