A crucial 121-run sixth-wicket stand between Gunaratne (80 not out) and Dickwella (81) secured Sri Lanka's best-ever run chase.
Sri Lanka's previous best was against South Africa in 2006, when they achieved a 352-run target. Tuesday's chase was also the highest in Asia and fifth best in Tests.
Man-of-the-match Gunaratne anchored the chase to perfection after Dickwella's departure, putting on an unbeaten 67-run partnership with Dilruwan Perera (29 not out) to take Sri Lanka to victory.
"It's always tough when you're batting in the fourth innings but I told the team that they should play their normal game and they played some outstanding innings, especially Dickwella and Asela," Chandimal said.
"It's always challenging as a captain but it's about doing the right things on and off the field," said Chandimal, who took over after Angelo Mathews quit because of the ODI loss.
Zimbabwe skipper Graeme Cremer claimed four wickets with his leg-spin to return overall figures of 9-275 at the R. Premadasa Stadium.
Wicketkeeper-batsman Dickwella rode his luck to reach 81 before being caught behind off left-arm spinner Sean Williams while attemping an audacious reverse sweep.
Dickwella survived a stumping chance from Sikandar Raza's off-spin on 37 and was then dropped by wicketkeeper Regis Chakabva on 63.
The stumping reprieve cost Zimbabwe dearly. It was referred to the third umpire, who ruled him not out despite replays showing his toe was on the crease -- a case where the batsman can be given out.
=================
Earlier, Cremer sent overnight batsman Kusal Mendis trudging back to the pavilion for 66 after Sri Lanka resumed on 170-3.
Cremer struck again with his leg-spin to have Mathews caught and bowled for 25. The visitors scented victory, but it was not to be for the 10th-ranked side.
"Credit to them...But the way the guys fought and got the runs on the board and pushed Sri Lanka till he last day was great," said Cremer.
"The one-day series is a high point for us, we brought that confidence into the Test match and it gave us the belief that we could push the big teams."
Zimbabwe batsman Craig Ervine's 160 in the first innings and allrounder Raza's 127 in the second essay were also notable performances in the match.
Sri Lanka host the number-one ranked India for three Tests, five one day internationals and a single Twenty20 later this month.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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