CELTIC 2 - 0 MOTHERWELL
Celtic secured the three points during an impressive second half spell and Sutton slid in to score the decisive goal from Alan Thompson's cross.
McNamara put Celtic in front after eight minutes with a fierce drive.
But there was bad news for the home side as Stilian Petrov was stretchered off with an ankle injury late on.
The match was preceded by the unfurling of SPL champions flags and a minute's silence for Celtic and Northern Ireland legend Bertie Peacock who died recently.
Celtic found the net first through an unlikely source after Motherwell dithered in defence in their own box and the ball found its way to Celtic skipper McNamara who hammered the ball across the face of Gordon Marshall in the Motherwell goal.
Martin O'Neill opted for Hartson and Sutton in attack and gave young Aiden McGeady a start on the right of midfield leaving new signing Henri Camara to warm the bench alongside Stephen Pearson.
Despite a capacity 60,000 crowd inside Celtic Park, the match was played out amid a subdued atmosphere as both sides suffered in the hot weather.
The home side had the best of the first half exchanges after taking the early lead, but Hartson spurned an early chance in the 12th minute as he sliced an attempted volley from a Sutton cross-field ball.
Motherwell failed to create many chances, but Alex Burns spurned one of their best opportunities when he headed over the bar in the 34th minute.
The visiting side ended the first half with a narrow escape after defender Shaun Fagan cleared a Sutton header off the line following a McGeady corner.
Celtic started the second half brightly, but John Hartson was again at fault when he wasted an excellent shooting chance on the edge of the box, preferring to pass the ball rather than go for goal.
The second goal arrived in the 55th minute after Sutton slid onto the end of Thompson's cross from a couple of yards out.
The game could have been over for Motherwell two minutes later after Sutton found himself bearing down on goal, but the English striker pushed a shot inches wide of Marshall's right-hand post with the goalkeeper beaten.
The final third of the game saw numerous subsitutions on both sides, with Camara making his SPL debut in the 66th minute in place of an exhausted Hartson.
The Senegal forward offered some flashes of skill, but failed to impose himself on the game after his last-minute winner against Newcastle in last week's friendly.
The game ended in worry for O'Neill as Petrov, who had looked impressive throughout, left the field on a stretcher with an ankle injury.
(Petrovs injury was only a twisted ankle..not too bad)
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Celtic: Marshall, McNamara, Varga, Valgaeren, Agathe, McGeady (Pearson 74), Lennon, Petrov (Sylla 88), Thompson, Hartson (Camara 67), Sutton. Subs Not Used: Hedman, Laursen, Wallace, Beattie.
Goals: McNamara 8, Sutton 55.
Motherwell: Marshall, Corrigan, Kinniburgh, Craigan, Hammell, O'Donnell, Leitch, Fagan (Fitzpatrick 71), Paterson, Burns (Foran 60), Clarkson (Scott McDonald 60). Subs Not Used: Corr, Partridge, Cowan, Keogh.
Att: 57,245
Ref: K Clark