His first-half header ensured Newcastle were able to leave behind the controversy over the on-field fight last Saturday between Kieron Dyer and Lee Bowyer, who received a rapturous welcome as a second-half substitute for his team mate.
Shearer broke the deadlock in the 37th minute when he was left unmarked near the penalty spot and headed in a Laurent Robert free kick from the left flank.
"It's a very good win, there was a lot of pressure on us for obvious reasons," 34-year-old Shearer told ITV. "We proved tonight we mean business. We want to go all the way and win it."
Midfielder Bowyer, who faces at least a four-game domestic ban after his weekend clash with Dyer in the match against Aston Villa, said of his reception: "It was really good. I couldn't have asked for more.
"I just asked for them to give me a chance and thankfully they've done that and hopefully I can repay them in the future."
Shearer, who last week decided to postpone his planned summer retirement for a year, took his Newcastle goal tally to 192, eight short of Jackie Milburn's record of 200 goals for the Tyneside club.
It was also the ex-England captain's 11th goal in eight UEFA Cup appearances this season and his 30th in European club competition, equalling ex-Leeds United player Peter Lorimer's British record.
Robert almost gave Newcastle a fortuitous lead when his corner just before Shearer's goal struck Ricardo's near post.
Early on Sporting had looked very comfortable against the English Premier League side, enjoying plenty of possession. But they were only able to trouble Shay Given once in the first half when Liedson tried his luck from distance.
Rui Jorge very nearly equalised just before the break when he dispossessed Dyer but his sweetly struck 25-metre shot flew narrowly wide.
Newcastle lost the services of goalkeeper Shay Given at halftime due to a hip injury and replacement Steve Harper did well to preserve his side's lead in the 66th with a fine save to keep out Joao Moutinho's shot.
REALLY DAFT
James Milner wasted an opportunity to double Newcastle's advantage late on when he latched on to a through-ball but lashed his shot over Ricardo's crossbar.
Sporting's cause suffered a major setback just before Shearer's goal when their Brazilian striker Liedson was booked for a rash challenge on full back Aaron Hughes.
He will be suspended for the return fixture next Thursday.
Hughes will also be missing after being cautioned by Russian referee Yuri Baskakov who also cautioned Bowyer seven minutes after his entry as a substitute for bringing down Sa Pinto.
Newcastle manager Graeme Souness was relieved to be able to concentrate on football after a difficult week in the wake of the Bowyer-Dyer incident. "I'm glad to get it out of the way," he said. "I'm just relieved that we've got through the game and we're talking about football again.
"At the end of the day they (Bowyer and Dyer) know they've been really, really daft. They won't do that again."
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