Sri Lanka 135 and 156 for 2 (Thirimanne 76*, Perera 62) trail England 421 (Root 228, Lawrence 73) by 130 runs

Sri Lanka's batsmen have earned themselves a chance of saving the first Test after a much improved performance on the third day in Galle.

Having endured a miserable first two days, Sri Lanka started their second innings with a deficit of 286. But after a first-innings display their batting coach, Grant Flower, rated as "the worst" he had seen, they demonstrated far greater resolve and application the second time around. Going into the fourth day, they have cut that deficit to 130 with eight second-innings wickets in hand.

A grim stat emerged after Sri Lanka's first innings. It suggested that Lahiru Thirimanne had the lowest average of any batsman in Test history (operating between 1-6, anyway) to play a minimum of 50 innings. And it's true, an average of 22.06 halfway through his 37th Test suggested he was somewhat fortunate to win another opportunity.

But here he went some way towards justifying his inclusion. In patiently accumulating an unbeaten 76, he not only recorded his highest Test score since March 2013 (when he made a century against Bangladesh on this ground), but exposed some vulnerability in an England attack who were flattered by the speed with which they accounted for Sri Lanka in the first innings.

In particular, England may be a little concerned by the performance of their spinners. For while Stuart Broad bowled with excellent control - he has conceded three from eight overs - and Mark Wood generated sharp pace from a sluggish surface, these are conditions in which spinners must be expected to do the bulk of the work. And on a surface on which their Sri Lanka counterparts gained sometimes sharp turn and bounce, Jack Leach and Dom Bess rarely threatened and managed only four maidens between them in 33 overs.

Bess, especially, struggled to settle into the required line and length, while Leach, though more threatening, conceded almost four-an-over for much of his spell and looked a little rusty. Perhaps that is not surprising given this was just Leach's third first-class game since December 2019 but the result was England's spinners failed to build much pressure. At times, Joe Root looked the most dangerous of them.

Sri Lanka's batsmen deserve some credit for that, of course. While Kusal Perera's aggression was his undoing in the first innings - he was caught at slip after attempting to reverse-sweep Bess' second ball - this time he took a more calculated approach to his positivity and made it tough for the spinners to settle, as a result. Leach, for example, was lofted for a straight six and, when he pulled back his length, slog-swept the next ball for four. The opening stand, 101, was not only the first century opening stand England had conceded since the MCG Ashes Test at the end of 2017, but the first time Sri Lanka's openers had survived more than 10 overs together in their most recent six innings.

How important a moment Perera's dismissal may prove remains to be seen. But, having made his third half-century in as many Tests since he was promoted to open, he failed to capitalise with another soft dismissal. Throwing his hands at a short, wide ball from Sam Curran, he succeeded only in picking out the man on backward point boundary.

Thirimanne could have gone in similar fashion. On this occasion, however, Dom Sibley, at gully, put down a straightforward chance when the batsman had 51. The looks of anguish on the faces of the England players spoke volumes.

Kusal Mendis, coming into the innings having suffered four successive ducks, at least made it to double figures. But when he went, drawn into a forward prod and caught behind as the ball spun to take the edge, it gave England - and Leach, in particular - an end of day boost.

Earlier, Root's double-century - the fourth of his Test career and his second as captain - helped England take a commanding first-innings lead by the time they were bowled out on the brink of lunch on the third day.

The ease with which Root amassed his runs might give a somewhat misleading impression about the nature of this pitch. But while Root appeared to find life straightforward - he was last man out, caught on the long-on boundary, attempting to set-up a declaration - it was noticeable that, after the first innings of both sides were completed, only two other men in the match had made more than 30. The last five in the England side contributed only 17 runs between them as Sri Lanka claimed six wickets in the morning session.

But Root looked comfortable throughout. Quick to size up the length of the ball and making liberal use of the sweep - a stroke that was very much a feature of this innings; CricViz have suggested Root's innings has contained more sweeps than any Test innings for which such data exists - Sri Lanka were never able to stop his flow of runs.

Only Wally Hammond (with seven) and Sir Alastair Cook (with five) now have more double-centuries for England. Root's score here represents the second-highest score by an England player in Asia after Cook's 263* in Abu Dhabi in 2015.

Root also surpassed 8,000 Test runs during the course of the innings. He is the seventh England player to reach the landmark and, in terms of innings (this is his 178th) the second quickest after Kevin Pietersen, who reached the milestone in 176 innings.

Asitha Fernando did provide a brief moment of joy for Sri Lanka, though. The seamer had only bowled nine of the first 100 overs in the innings but, immediately after an out of shape ball was changed, he gained some wicked late swing to claim wickets with two successive deliveries. First he took Buttler's edge with a full one which late him late, before persuading one to nip back between Curran's bat and pad to bowl him. Dom Bess negotiated the hat-trick ball securely enough but was run-out shortly afterwards as Root called him through for an impossible single, before Leach was tapped in front by a sharply-turning off-break and Wood miscued an attempted sweep and ballooned a catch to the keeper.

Broad survived being given out twice in three balls - umpire Kumar Dharmasena was forced to change his decisions after DRS showed neither of his LBW decisions were correct - and responded with successive boundaries off Fernando.

Meanwhile England received a boost off the field with the news that Moeen Ali had been released from isolation and was free to move to the team hotel. Moeen has been quarantined away from the rest of the tour party after testing positive for Covid-19 on arrival in Sri Lanka on January 3. He is unlikely to be considered for selection for the second Test as England take a cautious approach to his recovery.

George Dobell is a senior correspondent at ESPNcricinfo