Gloucestershire 195 for 5 (Charlesworth 58*, Hammond 50) trail Derbyshire 251 for 9 dec (Came 108) by 56 runs
The 24-year-old made 108 from 192 balls out of 251 for 9 declared with Matt Taylor and Ajeet Singh Dale both taking three wickets.
Although conditions were again overcast for most of the morning, Gloucestershire’s bowlers did not get the same amount of movement as they had the previous day and that made batting easier for Came and Reece.
Came again showed good judgement in selecting which balls to attack and passed his previous highest score of 78 made against Durham at Derby last season with a clip through midwicket
Reece had also looked comfortable until he drove at Taylor and edged to Charlsworth at slip to end a stand of 66 in 24 overs.
Came had one anxious moment when his scoop at Zafar Gohar just cleared the wicketkeeper but he reached three figures in style by driving the left-arm spinner over mid on for his 12th four.
There had been little for the Gloucestershire attack to celebrate and although Gohar had Alex Thomson caught behind pushing forward before lunch, it had been a good morning for Derbyshire and Came, who went in unbeaten on 106.
The opener’s excellent innings ended in the second over of the afternoon session when Henry Brookes called him through for a sharp single and he failed to beat Chris Dent’s throw from cover to Bracey.
When Sam Conners steered Singh Dale to second slip, Derbyshire were in danger of missing out on a batting point but Lakmal secured it with a couple through midwicket and then delivered his best spell of the season.
The Sri Lankan beat Marcus Harris and Dent several times and bowled six consecutive maidens to build pressure which eventually told on the Gloucestershire openers.
Dent, who had been missed at fourth slip off Conners on 8, tried to cut a ball from Lakmal that was too close to him and played on.
Reece had also given nothing away and Harris lost patience in the next over when he flashed at a ball he could have left and was caught at second slip.
Lakmal’s stranglehold was broken when Hammond drove him through the covers for four, the first runs he conceded for 39 balls, and he took his sweater with the outstanding figures of 1 for eight from eight overs.
Hammond and Charlesworth rebuilt the innings with the former reaching his 50 by launching Thomson over long on for six but the return of Reece plunged the visitors back into trouble.
A ball which lifted just enough to take Hammond’s outside edge flew to gully where Haider Ali took a fine catch plunging to his right and the next delivery moved away from Graeme Van Buuren who was caught behind.
Charlesworth and Bracey responded with a stand of 79 from 115 balls which was ended when Bracey was lbw pulling Henry Brookes but at stumps, Gloucestershire were only 56 behind.