Celtic manager Martin O'Neill took some consolation from yesterday's 2-0 defeat by Dundee at Parkhead with the news he had scooped the Scottish manager of the year award.
The champions suffered their first home defeat this season after Fabian Caballero's first-half double strike.
Argentinian striker Caballero emerged from the shadows of countryman Claudio Caniggia to give 10-man Dundee a well-deserved victory. Caniggia is expected to complete his move to Rangers this week, but Caballero, however, grabbed his opportunity with goals either side of Zura Khizanishvili's sending off.
The champions, who will attempt to complete a domestic treble when they face Hibernian in the Scottish Cup final in a fortnight, must now win their final day of the season trip to Kilmarnock to become the first Scottish Premier League side to reach 100 points in a season.
Record-breaking striker Henrik Larsson had another milestone in his sights as he aimed to beat Brian McClair's top-flight scoring feat of 35 in season, but he endured a rare off day. The home crowd were stunned on the half hour when Celtic fell behind. Gavin Rae found Beto Carranza on the left and he played the ball to Caballero, who turned away from Valgaeren before curling an inch-perfect effort past Gould into the bottom corner.
But Celtic were thrown a lifeline three minutes later when Dundee were reduced to 10 men. Khizanishvili attempted to pull down Larsson, but the Swede shrugged him off to shoot just wide of the post. Referee Tom Brown pulled play back and brandished the red card. The blow failed to knock Dundee and they doubled their lead two minutes before the break. Javier Artero found space on the right wing and played the ball across the face of goal. Caballero was the first to react and shot home from close range, with Ramon Vega dithering.
Dundee, however, were fortunate not to concede a penalty on 73 minutes when Larsson seemed to be hauled down, but referee Brown waved away the protests.
Then Moravcik, who had scored four goals in three games before yesterday, somehow headed wide from five yards after Thompson's dangerous corner.
Alan Stubbs, who scored on his comeback from cancer last week, replaced Valgaeren to a standing ovation. But he was booked for retaliating to Caballero's theatrical dive in the 83rd minute.
Celtic: Gould; Vega (Boyd 46), Mjallby, Valgaeren (Stubbs 80), McNamara, Lennon, Lambert, Moravcik, Thompson, Smith (Maloney 46), Larsson. Subs Not Used: Kharine, Healy. Booked: Stubbs.
Dundee: Langfield; Smith, Khizanishvili, Coyne, Del Rio, Artero (Garrido 68), Romano, Rae, Robertson, Carranza, Caballero (Milne 86). Subs Not Used: Soutar, Sara, Fatello. Sent Off: Khizanishvili (34). Booked: Robertson, Caballero. Goals: Caballero 29, 42.
Referee: T Brown (Scotland).