Replying to India's imposing 155 for six, Ireland 54 for two when rain ended play, handing India a rain-adjusted five-run win.
A strong, swirling wind made conditions difficult and Mandhana was dropped four times in the outfield during a 56-ball innings which included nine fours and three sixes.
Shafali Verma made 24 and helped Mandhana put on 62 for the first wicket but both batters struggled initially to time the ball, although Mandhana hit with authority after reaching her half-century off 40 balls.
Indian captain Harmanpreet Kaur, playing in her 150th T20 international, became the fourth player to reach 3000 runs in the format but also lacked fluency before being dismissed for 13 off 20 balls.
While other bowlers suffered from dropped catches, Ireland captain Laura Delany benefitted from three good catches in the deep to take three for 33.
One of the catches was held by a diving Orla Prendergast, who also bowled impressively to take two for 22.
Ireland made a disastrous start when Amy Hunter was run out off the first ball of the innings, attempting a second run after hitting the ball to midwicket.
Four balls later Prendergast was bowled by Renuka Thakur without scoring.
But Gaby Lewis (32 not out) and Delany (17 not out) shared a spirited unbeaten partnership of 53.
With rain threatening, they went for their shots, raising the possibility of an upset win if they went past the adjusted par total.
But when the rain became heavier, play was halted and eventually called off.
India finished the group stage with three wins from four matches and will face Australia in the semi-finals in Cape Town on thursday.
Ireland, let down during the tournament by some indifferent fielding, lost all their matches.
England, who play Pakistan in Cape Town on Tuesday, have also qualified for the semi-finals and will finish top of the group if they win.
Brief scores:
India 155-6 in 20 overs (S. Mandhana 87; O. Prendergast 2-22, L. Delany 3-33)
Ireland 54-2 in 8.3 overs (G. Lewis 32 not out)
Result: India won by 5 runs (Duckworth/Lewis method)
Toss: India
