With Rotherham United not playing due to Reading's FA Cup commitments, Wigan went into Saturday's game knowing anything less than a win would result in them being demoted to League One.
Caldwell - who replaced Malky Mackay earlier this month - looked set to see his side suffer the drop after Brighton's Dale Stephens had cancelled out debutant Tim Chow's header for the hosts.
But James Perch struck from close range nine minutes from time to keep Wigan's slim hopes of survival alive, while third-bottom Millwall failed to move within two points of Rotherham as they drew 0-0 at Cardiff City.
At the other end of the table, the race for promotion remains extremely tight, with Watford going top as Bournemouth slipped up.
Craig Cathcart's volley gave Watford a 1-0 win over Birmingham that sees them leapfrog Middlesbrough and Bournemouth - who drew 2-2 at home with Sheffield Wednesday.
Meanwhile, Derby County missed the chance to capitalise on the 1-1 draw between Wolves and Ipswich Town and Brentford's 2-2 stalemate with Bolton Wanderers and put more daylight between themselves and their play-off rivals.
Steve McClaren's men played out an enthralling 4-4 draw at Huddersfield Town. Nahki Wells put the Yorkshire club 4-3 up in the 72nd minute after Derby had fought back from 3-1 down, only for Tom Ince to rescue the visitors with his second.
Fulham are all but safe after a 1-0 win at relegated Blackpool, while Michail Antonio salvaged a 3-3 away draw for Nottingham Forest versus Blackburn Rovers after Rudy Gestede's hat-trick.
Elsewhere, Charlton Athletic beat Leeds United, whose striker Billy Sharp missed a 36th-minute penalty - 2-1.
