The first Test between Bangladesh and Sri Lanka ended in a draw at Zahur Ahmed Chowdhury Stadium, Chittagong on Thursday.
On the fifth and final day the two teams settled on a draw 45 minutes before the scheduled close of play with Sri Lanka on 260-6 in their second innings.
Dickwella was unbeaten on 61 alongside Chandimal on 39 not out at the Zahur Ahmed Chowdhury Stadium.
Hosts Bangladesh made 465 in their first innings in reply to Sri Lanka's 397 as Tamim Iqbal (133) and Mushfiqur Rahim (105) played starring roles.
Angelo Mathews hit 199 to form the backbone of the Sri Lankan first innings and Nayeem Hasan claimed 6-105 for Bangladesh.
On Thursday left-arm spin duo Taijul Islam and Shakib Al Hasan had given Bangladesh hope of victory with early strikes, before Chandimal and Dickwella thwarted the home side.
Sri Lanka skipper Dimuth Karunaratne made 52 off 138 balls before he gave a catch to his counterpart Mominul Haque at midwicket off Taijul.
Shakib soon had Dhananjaya de Silva out for 33 off 60 balls as Mushfiqur Rahim took the catch, also at midwicket, leaving Sri Lanka reeling at 161-6.
Dickwella swept the next ball high but Taijul could only manage to get a finger on it at square leg. After the scare, he and Chandimal then dug in at the crease before and after the tea break.
Taijul struck twice in the morning session after Sri Lanka started aggressively, resuming on 39-2.
Taijul bowled Kusal Mendis for 48 and then removed first-innings centurion Mathews for a duck, caught and bowled.
Taijul was the pick of the bowlers with innings figures of 4-82.
Bangladesh were one bowler short on the fifth day after paceman Shoriful Islam was ruled out of the two-Test series following a blow he received on his hand while batting on Wednesday.