In 295 one-day internationals before the Sri Lanka-Zimbabwe series began, no team had chased the 300-plus total in Sri Lanka.
While Zimbabwe's win gave them their first ever win over Lanka in any format, the home team's win by eight wickets in Hambantota on Thursday gave them a 2-1 lead in the five-match series.
Dickwella (102) was dropped on 64 before racing to his maiden ODI hundred before sweeping Malcolm Waller to deep square leg.
"It was a fantastic effort by the boys", said Angelo Mathews, the Sri Lanka skipper. It was a great wicket to bat and we knew if we played our natural game, we could get it easily.
Upul Tharanga (44) and Kusal Mendis (28) then steered the team home with an unbeaten 75-run stand as the batting duo survived a dropped catch each as fielding lapses also hurt the visitors.
No other Zimbabwe batsman could get passed fifty though and they will feel they missed out on an absolute road.
"The bowlers came back pretty well after the start that they (Zimbabwe) got".
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Earlier Masakadza put on a crucial 127-run partnership for the second wicket with Tarisai Musakanda (48) before Sri Lankan bowlers struck back to check Zimbabwe's surge.
Masakadza made 111 from 98 balls, hitting 15 boundaries and a six in his fifth ODI century.
Sean Williams was at his usual best, scoring a handy 43 andm with the help of that and the lower-middle order, Zimbabwe posted a challenging 310 for 8 in 50 overs.
Wanindu Hasaranga, the teenaged legspinner who took a hat-trick on his ODI debut in the second match in Galle, and Asela Gunaratne, the medium pacer, grabbed two wickets each.
"We need to get runs on the board batting first, but 310 was enough, we just need to get better with the field.Our bowling was probably under par (as well)", Zimbabwe skipper Graeme Cremer said.
The action now shifts to the fourth ODI on Saturday at the same venue.