Bojan Kaljevic scored in the 70th minute to become the club's hero yesterday evening.
His goal enabled Mosta to return to winning form after five consecutive defeats.
It was definitely a positive debut for new Mosta coach Peter Smith. He was appointed in the last few days after Enrico Piccioni was dismissed by the club.
The Blues have now moved onto the 16-point mark while Tarxien remain on 12 points.
In the first half play was more or less lively with Mosta, however, showing the better ideas and creating the most clearcut opportunities.
Tarxien also had their moments, but found Omar Borg in top form. Moreover, Tarxien were not as sharp as Mosta were up front, even if Jorge Santos Silva was a constant headache for the Malta defence.
In the second half, Tarxien were a transformed side and quickly took the game to their opponents. It seemed as if Barbosa Viana's introduction made all the difference as he became a protagonist, also scoring the temporary equaliser for his side.
Tarxien were not happy at all with a drawn result, but in their efforts to take the lead, they left their backdoor open and Mosta made the most of a misunderstanding in the Rainbows defence to take the lead again through the dangerous Kaljevic.
The Blues had an electrifying start when Kaljevic entered the area only to see his shot saved by Sean Mintoff.
At the other end, a Triston Caruana freekick created havoc in the Mosta area, but the ball was eventually cleared to safety.
It was Mosta, however, who took the lead on the 12th minute. Kaljevic crossed from the right. Ekani squared low into the area where Micallef was on hand to tap the ball home.
In the 23rd minute, Hevia Menendez forced Mosta goalie Omar Borg into a fine save, turning the ball to a corner.
A few minutes later, from a Menendez cross, the ball arrived at Tabone's feet, but the latter's scissors kick went wide.
On 30 minutes, Kaljevic set Calcado in the Tarxien area, but the latter's shot was well saved by Mintoff. The ball rolled out to Kaljevic but this time the Mosta striker's effort was weak and Mintoff could save with ease.
Two minutes later, it was Magro who tested Mintoff, but the Tarxien goalie was equal to the task.
In the 36th minute, Omar Borg was called upon to block a Lima Silva shot from the angle.
Before the interval whistle, Bueno crossed into the area but Mano Micallef's header was saved by the diving Mintoff.
At the start of the second half, Tarxien appeared to be more aggressive and on the 49th minute, it was substitute C. Barbosa Viana who had a fine shot going close. Soon after, Omar Borg blocked on Barbosa once again - the latter's presence seemed to have revitalised the Tarxien frontline.
In fact, in the 53rd minute, it was Barbosa who equalised for the Rainbows, finding the net with a rising shot from the angle.
Tarxien insisted and four minutes later, Lima Silva saw his freekick just missing the target.
In the 64th minute, in a swift counter-attack, Tarxien again went close through a Lima shot which hit the upright.
Despite everything, it was Mosta who regained the lead on the 70th minute as Kaljevic made the most of a misunderstanding in the Tarxien defence to hit home.
At the other end, in a swift reply, it was Borg who denied Tarxien an equaliser, saving a Barbosa Viana effort.
In added time, Kaljevic was again dangerous in the Tarxien area, but goalie Mintoff blocked his effort to a corner.

Qormi and Pieta shared the spoils in what must have been the most boring match of the season so far.
The goalless draw seemed to have been the most probable result for most of the time, except on a few occasions in the second half.
Pieta moved on to the eight point mark while Qormi now have 15 points.
Pieta had Darren Agius missing from their line-up, while for Qormi, Frank Temile was returning to the side after injury.
The first half was scarce for actions as a lot of midfield play ensued. Neither team showed superiority and the two goalkeepers were rarely in action. In fact, they were only called upon to effect some easy saves on a few shots from a distance except on one occasion, early on, when Pieta goalie Cassar blocked on Frank Temile.
Qormi perhaps saw a little more of the ball, but both Effiong and Temile were far from their best form and were easily controlled by a strong Pieta rearguard.
The Hotspurs showed better ideas up front whenever they attacked, but were found wanting when they came to conclude; so much so that Qormi goalie Matthew Farrugia was never really tested.
The second half was much better than the first even if the level of play remained low especially from the technical point of view.
Qormi remained slightly superior. While they attacked a lot more than Pieta, however, Pieta defended stubbornly although it was the post, on one occasion, and goalie Cassar, with an excellent save, that kept their goal intact.
Pieta also had a few good moments, but these were quite few and also far between.
The first action worthy of note arrived on the 13th minute. From a Quatrochi Santos pass, it was Frank Temile who came face to face with goalie Cassar, but the Pieta goalie somehow managed to block with his feet.
On the 28th minute Frank Temile's low effort from 20 metres was easy prey for goalie Cassar.
Five minutes later, at the other end, it was Frances who tried his luck from the distance, but his effort went wide. In the 37th minute, Zacarias went round a defender on the edge of the area, but his shot went wide.
The second half started with Qormi on attack. From a Temile cross, Ryan Micallef controlled the ball well, but his shot was blocked by a Pieta defender.
In the 53rd minute, it was Quatrochi who had an effort going over the bar. And as Qormi intensified their pressure, it was Effiong who had a shot deviated onto the post with the ball being eventually cleared to safety.
At last, Pieta also had their good moment when in the 66th minute, Fortunato dos Santos squared the ball to the unmarked substitute Orosco Anonam, but the latter hit well over the bar from an ideal position.
On 77 minutes Qormi went close to open the scoring when Quatrochi brought the best out of goalie Cassar, the latter turning the ball away from a fierce shot from the Qormi player.
Qormi insisted and Duncan Pisani also had a shot going over the bar. That was the last action of a match which both sides need to forget quickly about.
At the end, the goalless draw was a fair result.