The pair's clash had gone to a third day with the inclement weather buffeting the Thai beach resort severely disrupting play.
But with a brief interlude allowing action to finally recommence, Serb Ivanovic started on serve at 2-1 down in the third set.
It was Morita who appeared less affected by the delays however, the Japanese holding firm in the remainder of her service games, while breaking Ivanovic, crucially, just once.
Morita wen on to beat evergreen veteran and compatriot Kimiko Date-Krumm in the second round in the evening.
Heather Watson was seeded eighth for the tournament but fell to Latvia's Anastasija Sevastova, who sits 143 places below the 40th-placed Brit in the world rankings.
Watson fought back from having her serve broken in the first game to force a tie-break but lost the opening stanza before hitting back to take the second set.
However she was overpowered by the underdog in the third, holding serve only once.
2-Maria Kirilenko (Russia) beat Luksika Kumkhum (Thailand) 5-7 6-2 6-2
4-Sorana Cirstea (Romania) beat Anastasia Rodionova (Australia) 6-0 7-6(3)
5-Sabine Lisicki (Germany) beat Alexandra Panova (Russia) 7-5 6-2
Nina Bratchikova (Russia) beat 6-Daniela Hantuchova (Slovakia) 6-2 3-0 (Hantuchova retired)
7-Elena Vesnina (Russia) beat Mathilde Johansson (France) 6-2 3-6 6-1
Anastasija Sevastova (Latvia) beat 8-Heather Watson (Britain) 7-6(4) 4-6 6-2
Ayumi Morita (Japan) beat Kimiko Date-Krumm (Japan) 4-6 6-4 6-1
Marina Erakovic (New Zealand) beat Varatchaya Wongteanchai (Thailand) 6-3 7-6(4)
6-Daniela Hantuchova (Slovakia) beat Olga Puchkova (Russia) 6-1 3-6 6-0
7-Elena Vesnina (Russia) beat Eleni Daniilidou (Greece) 6-2 5-7 6-2
Ayumi Morita (Japan) beat 1-Ana Ivanovic (Serbia) 6-3 5-7 6-3