The sides were level at half time 0-5 to 1-2, with the Cavan goal coming in the 12th minute when Westmeath goalkeeper Darren Quinn badly misjudged a Seanie Johnston effort.
Westmeath raised their game after the break and Dessie Dolan struck four points in 16 minutes.
Overall, Cavan will rue their poor shooting, which resulted in a total of 12 wides.
However, they stayed in touch and even when Westmeath led by two points entering the final five minutes, they hit back with two points from substitute Gearoid McKiernan to earn a deserved draw.
Westmeath midfielder John Heslin was sent off deep into injury time for a straight red card offence and will be a major loss for the county’s Under 21 side in their Leinster championship match against Laois on Wednesday.
Scorers for Westmeath: D Dolan 0-4 (two from frees), P Greville 0-2 (two from frees), J Heslin 0-2, Denis Glennon, F Wilson, G Egan, D Corroon 0-1 each.
Scorers for Cavan: S Johnston 1-3 (one point from a free), G McKiernan 0-2, M McKeever 0-1, G Pearson 0-1, R Flanagan 0-1 (one from a free), R Cullivan 0-1 each.
WESTMEATH: D Quinn; F Boyle, K Gavin, J Gaffey; A Finnan, K Martin, D Harte; D Corroon, J Heslin; F Wilson, Denis Glennon, G Egan; P Greville, David Glennon, D Dolan.
Subs: C Lynam for Denis Glennon (42), P Tormey for P Greville (55), S Quinn for F Wilson (59), J Dolan for A Finnan (63), J Connellan for David Glennon (68).
CAVAN: J Reilly; A Clarke, P Carroll, S Jordan; M McKeever, J McCutcheon, D O’Reilly; R Cullivan, P O’Reilly; K Fannin, N Murray, R Flanagan, S Johnston, G Pearson, B Fitzpatrick.
Subs: M Cahill for D O’Reilly (31), C Mackey for B Fitzpatrick (h-t), G McKiernan for K Fannin (h-t), D Givney for N Murray (44), B Reilly for J McCutcheon (57).
Referee: M Sludden (Tyrone).