The Indians triumphed by eight wickets at the Qadhafi Stadium after being set a modest target of 158.
Jain hit an 85 ball-59 with eight fours while Deshpande remained undefeated with 57. Her 92-ball innings contained eight boundaries. The pair added 122 for the second wicket.
Earlier, Pakistan skipper Shamsa Hashmi played another good knock of 51, while striking six fours and one six and faced 81 balls.
Apart from Shamsa, opener Taskeen Qadeer contributed 44 off 70 deliveries with the aid of eight boundaries.
The fourth and final match will be played at the same venue on Sunday.
Scoreboard
PAKISTAN:
Sana Javed c Karuna b Dhar 0
Taskeen Qadeer c and b David 44
Nabila Gulzar b Nath 12
Urooj Khan c Karuna b Nath 0
Shamsa Hashmi c Karuna b Nirala 51
Arman Khan st Karuna b David 0
Mariam Butt lbw b Dhar 16
Sana Mir run out 5
Asmavia Iqbal not out 10
Qanita Jalil run out 0
Sabahat Rashid run out 2
EXTRAS (LB-3, W-14) 17
TOTAL (all out, 38.5 overs) 157
FALL OF WKTS: 1-0, 2-30, 3-30, 4-106, 5-106, 6-136, 7-138, 8-145, 9-150.
BOWLING: Rumeli Dhar 6-0-19-2; Soujanya Nath 5-0-25-2; Niramana Nasarajan 4-0-26-0; Savitha Nirala 7-0-36-1; Priti Dimri 5-1-10-0; Diana David 6.5-1-19-2; Sravanthi Naidu 5-0-19-0.
INDIA UNDER-21:
Karuna Jain c Sana b Urooj 59
Shweta Jadhav lbw b Qanita 0
Anagha Deshpande not out 57
Rumeli Dhar not out 19
EXTRAS (LB-1, W-22) 23
TOTAL (for two wkts, 32.5 overs) 158
FALL OF WKTS: 1-9, 2-131.
DID NOT BAT: S Nath, Niranjana, Savitha Nirala, Priti Dimri, Diana David, Sravanthi Naidu, P Sindhu.
BOWLING: Mariam Butt 5-0-19-0; Qanita Jalil 4-0-27-1; Shamsa Hashmi 6-1-22-0; sana Javed 3-0-19-0; Urooj Khan 7-0-31-1; Sabahat Rasheed 5-0-15-0; Asmavia Iqbal 2-0-15-0; Sana Mir 1-0-9-0.
RESULT: India Under-21 won by eight wickets.
UMPIRES: Rasheed Bhatti and Zameer Haider.
MATCH REFEREE: Abdul Sami Khan.