Captain Pat Horgan saved Cork’s blushes with 2-8 in Mullingar as the Rebels moved joint top of Group A.
But Cork are only temporarily on top as this was the only game in the group to go ahead - and they flirted with disaster at TEG Cusack Park.
Leading 0-7 to 0-1 after 20 minutes with a big wind behind them, Cork were outscored 1-13 to 3-5 from there on in stormy conditions.
Horgan’s goals in the 38th and 61st minutes were decisive and both came from penalties.
But the visitors were painfully unable to impose themselves and three late Allan Devine frees left Westmeath just three behind in stoppage time.
Horgan ultimately settled it with a 73rd minute point from a free as Cork, who hit Westmeath for 1-40 in last summer’s Championship, limped over the winning line.
Both teams finished with 14 players after Damien Cahalane and Westmeath’s Joey Boyle were dismissed in the 42nd minute.
Cahalane was dismissed on a straight red which will carry a one-match ban while Cork also lost Conor Lehane to an early hamstring injury.
Lehane was on form with two points and his departure appeared to affect Cork who lost their way after the 20-minute mark.
Cork: P Collins; S O’Leary Hayes, E Cadogan, C Spillane; T O’Mahony (0-1, 1 s/l), B Cooper (1-0), D Cahalane; C O’Leary, L Meade (0-1); A Walsh, J O’Connor, C Lehane (0-2); D Dalton, P Horgan (2-8, 2-0 pen, 7f, 1 65), S Harnedy.
Subs: S Twomey for Lehane 12, R Downey for Twomey 48, N O’Leary for Walsh 52, B Turnbull for O’Connor 59.
Westmeath : A McHugh; C Shaw, T Doyle, A Ennis; A Craig, A Clarke (0-1), L Varley; C Boyle, E Price; J Boyle (0-1), D McNicholas (0-2), R Greville; N Mitchell, A Devine (1-8, 1-0 65, 7f), C Doyle.
Subs: D Clinton (0-2) for Mitchell 44, K Doyle for C Doyle 52, A Cox for Shaw 54, S McGovern for Greville 57, B Doyle for Ennis 64.
Ref: L Gordon (Galway).
