Tbilisi were never in the hunt and only some poor finishing denied United a healthy return of goals.
But it was the win that was all-important as Newcastle again kept a clean sheet against foreign opposition – making it three in four starts this season.
Newcastle named an attacking formation with Bellamy forced to play in midfield again as Graeme Souness went for the strike pairing of Patrick Kluivert and Shearer as he looked to maintain his 100 per cent record at St James' Park.
Tbilisi, the lowest ranked side still in the competition, found themselves in early trouble when Kluivert turned well after linking with Laurent Robert only to see his shot take a deflection and drop back to keeper Zurab Mamaladze.
In the first of four successive home games in three different competitions, Kluivert then tested the keeper with a low drive following good work from the industrious Jermaine Jenas.
Georgi Shashiashvili was cautioned after seven minutes before Newcastle strung together a flowing move that again involved Kluivert, who found skipper Alan Shearer and then the incoming Bellamy, who fired wide.
Kluivert had a great opportunity to open the scoring on the quarter-hour mark. Bowyer raced back to stop a visiting attack, then popped up at the other end to clinically pick out Kluivert, who should have done better before Shashiashvili whipped the ball off his toes.
United then broke on a three-to-one situation with Jenas crossing from the left for Kluivert, who cleverly dummied for Bellamy, but the Welshman was let down by his first touch and his eventual shot was blocked.
This was the first time that Robert, Shearer, Kluivert and Bellamy had all started a home game - the only other time the quartet started produced a five-goal haul earlier in the competition in Tel Aviv.
On the back of three successive defeats, Tbilisi were constantly on the back foot, but must have been delighted when they managed to hold Newcastle in the opening half hour, and that after Levan Melkadze forced Shay Given to tip his right foot drive over the bar.
Lasha Salukvadze then almost put through his own goal under pressure from Kluivert as he attacked a Robert free-kick, but Newcastle failed to produce the expected early landslide.
A Given goal kick left Robert in the clear after 35 minutes but in trying to pick his spot the Frenchman shot well wide.
Given was then involved again three minutes later as Shearer emphatically struck his 22nd European goal and his 182nd for United overall.
Robert headed inside for Kluivert, whose threaded pass was latched on to by Shearer in the inside-right position and the skipper rocketed the ball into the back of the net.
It was just the tonic United needed and they almost grabbed a second when good link work between Bellamy and Robert saw a cross from the Frenchman pick out Kluivert and his header went agonisingly close with the keeper beaten.
Newcastle gave themselves some breathing space after 56 minutes as Bellamy struck for the first time in Europe this season.
Robert's right wing corner saw Mamaladze outnumbered and the keeper only succeeded in palming the ball into the air for Giorgi Nemsadze to miscue a headed clearance - allowing Bellamy to volley home from ten yards.
Robert had a free-kick clawed out by the keeper after 72 minutes and, from the resulting cross, Shearer headed in, only for the goal to be disallowed for offside. Television replays showed it was poor decision.
Denied a second goal, Shearer made way seconds later for James Milner, with Souness clearly thinking of Sunday's game with Fulham.
Milner made a magnificent attacking run but saw his shot blocked and Robert found himself in a good shooting position but pulled his effort wide.
Tbilisi never showed any qualities to get themselves back into contention and it was left to Newcastle to dominate proceedings, but they lacked the necessary cutting edge to add to the score line.
Robert's late surging run saw the keeper push his effort behind, before Jaba Kankava popped up on the line to deny Kluivert a goal in time added on - a goal would have been just reward for the Dutchman's fine technical display.