Former England keeper Robinson was called into early action, scrambling across his line to spare Chris Samba's blushes after the Rovers defender almost put the ball in his own net.
McCarthy, linked with a move away from Ewood Park in January, then netted his first Premier League goal of the season on the half-hour mark to give Rovers the lead.
The South African forward was on hand to turn home from the edge of the six-yard box as he converted Ryan Nelsen's header on, to leave Wigan keeper Chris Kirkland stranded.
Wigan finally sprung to life on the stroke of half-time when Jason Scotland stung Robinson's palms but the hosts were much-improved after the break.
On 53 minutes, Scotland held the ball up well and fed the lively Charles N'Zogbia, who crossed for Colombia forward Rodallega to head home his seventh league goal of the season.
N'Zogbia threatened again just minutes later, again bursting through on the overlap before rifling a low left-footed shot just past Robinson's left-hand post.
With ten minutes remaining, McCarthy might have pinched the points with an acrobatic overhead kick from Samba's flick-on, but Kirkland produced an excellent reaction save to keep the scores level.
In the dying stages, Blackburn resorted to route one football but it almost paid dividends for Sam Allardyce's men as Keith Andrews shot just wide after the Wigan defence had failed to clear their lines.
And McCarthy almost latched onto another flick from Samba following Robinson's clearance as Rovers laid siege to the Latics goal but Roberto Martinez's side held firm to grind out a point.