At tea, England were 173 for seven, still needing a further 177 runs to reach their victory target of 350.
But the more realistic goal was to preserve their last three wickets in the minimum 40 overs that remained to secure a draw, with the new ball available to Sri Lanka three overs after tea.
Root, six not out overnight, got under the skin of his opponents with his verbal taunts in the field.
Together with Moeen Ali (56 not out), Root kept Sri Lanka at bay for more than two hours Tuesday until Nuwan Pradeep -- whose tailend feat in surviving the final five balls saw the tourists to a draw in the first Test of this two-match series -- made the breakthrough.
Root, looking to turn a full-length delivery legside, got an outside edge off Pradeep and was caught in the gully by Lahiru Thirimanne for 31.
Sri Lanka thought they had him caught on 52 at leg slip off left-arm spinner Rangana Herath but Davis ruled not out and a review confirmed the Australian's decision.
Nevertheless England, who resumed Tuesday in the dire position of 57 for five after Dhammika Prasad's four-wicket burst late Monday, saw the paceman strike again before tea.
