Celtic looked set for their second victory of the season after a first-half goal from Stilian Petrov.
Motherwell's case was not helped by the sending off of John Davies for two bookable offences.
The Celtic supporters gave a warm welcome to new manager Martin O'Neill and new signings Chris Sutton and defender Joos Valgaeren, who were making their home debuts.
O'Neill, who lost out on a move from Manchester United goalkeeper Mark Bosnich yesterday, was able to call on the same side that beat Dundee United last Sunday, with the exception of injured defender Alan Stubbs, who was replaced by Ivory Coast stopper Oliver Tebily.
Sutton continued his partnership with Swedish striker Henrik Larsson after both hit the target at Tannadice while Lubo Moravcik and Johan Mjallby came onto the bench after suspension and injury respectively.
Victory for Celtic was no certainty against a Motherwell side, who shocked the Parkhead side here last season.
Billy Davies' outfit were looking to bounce back from defeat at home to Dundee last week and welcomed striker Lee McCulloch back from suspension, while new boy Ange Oueifio had to settle for a place on the bench.
The visitors started impressively and were causing the Celtic defence problems early on with Paul Harvey being given acres of space to try a shot from the edge of the box that Gould could only parry.
Gould got the nod over Stewart Kerr again in the Celtic net despite a shaky display in the victory at Dundee United.
Motherwell midfielder Davies' over-enthusiasm cost him a booking in the fifth minute when he brought down Petrov with a reckless challenge near the by-line, but they were making it difficult for Celtic early on.
Valgaeren could have grabbed a glory goal on his home debut in the eighth minute when he met Petrov's free kick at the far post but he could not direct his header on target.
Celtic started to stamp their authority on the game and in the 11th minute they took the lead in emphatic style.
There was a moment of hesitancy in the Motherwell defence as Jackie McNamara played the ball to Petrov, who drilled a 25-yard right-footed shot past a rooted Goram.
That fired up the visitors and Gould had to be alert to save a fierce effort from Martin Corrigan in the 12th minute.
Celtic looked a side full of confidence going forward following the goal and the visitors were under pressure when defender Greg Strong fouled McNamara in the 23rd minute just outside the box.
From the resulting freekick Petrov rolled the ball back to McNamara on the edge of the box and the wing-back fired just over the bar.
Three minutes later Valgaeren threatened again in a dead-ball situation, heading McNamara's freekick over the bar as the home side pressed forward in search of a second goal.
Celtic defence still looked nervous on occasions and Motherwell refused to lie down.
But the home side still looked dangerous going forward and Stephane Mahe, Larsson and Sutton linked up well to create a chance for Eyal Berkovic in the 34th minute only for the Israeli international to drag his shot wide.
However, Motherwell's hopes of getting back on level terms in the match were dealt a massive blow in the 37th minute when Davies petulantly pulled back Petrov and the referee Alan Freeland flashed the yellow card, followed by the red.
The home side could have capitalised from this almost immediately when Sutton shook off the challenge of Benito Kemble before playing the ball into the path of Berkovic but he was slightly off balance and failed to find the direction to beat Goram from 12 yards.
Kemble became the next Motherwell player into the referee's notebook after 41 minutes following a late tackle on Larsson.