Though Andy Fenby replied with a try for the visitors just two minutes after Goodman's, Leinster were always in control and Aaron Dundon and Jordi Murphy added further tries, before a bonus point was delivered by John Cooney at the very end of the game.
Just three points had separated Leinster in third, and fourth-placed Scarlets before the game, and the importance of a victory had not been lost on either camp during the build-up.
So Goodman would have eased any nerves when he got Leinster's first points on the board in just the third minute, coolly kicking a penalty through the posts.
From that moment the hosts remained in the ascendancy early on, dominating possession but failing to break through the Scarlets defence for an early try.
The visitors weren't helped when lock George Earle was sent to the sin bin in the 16th minute, but there followed a spell of pressure from Scarlets despite their disadvantage.
Fly-half Owen Williams and scrum-half Aled Davies were seeing plenty of ball and attempted to gain territory with a series of kicks to touch, but the hosts repeatedly held firm and it wasn't long before they began to dominate possession once more.
Williams missed a 21st-minute penalty for Scarlets, prompting a series of Leinster attacks, though the men in red continued to remain difficult to break down.
The game was developing into a scrappy affair around the mid-way point of the first half, with several penalties given away by both sides as referee Marius Mitrea repeatedly penalised infringements at the ruck.
On the half hour, Leinster doubled their lead as centre Goodman struck home his second penalty from the right of the posts after a good spell of pressure.
Given the difficulties the home side had breaking down Scarlets in the opening stages of the game, you sensed it would take a moment of real quality to bring the game's first try - and that is exactly what happened as Leinster increased their lead to 11-0.
It was a fine passage of play from Joe Schmidt's men as wing Fionn Carr picked up possession in the middle of the park and switched play to the right-hand side. A series of quick passes avoided Scarlets challenges before Dave Kearney fed the ball back inside to the onrushing Goodman who surged into the corner and over the try-line under the challenge of Davies.
Scarlets' response however was immediate. After Goodman missed the conversion attempt, Davies found Fenby in acres of space, allowing the wing to ease into the corner and score his side's first points, though Williams was unable to add the extras.
With Goodman receiving treatment, fly-half Noel Reid took over penalty duties for the hosts four minutes before the break, but missed a simple attempt when his kick from a central position cannoned back into play off the posts, and there was still time for Goodman himself to miss another penalty with the last kick of the first half, leaving the scoreline at 11-5.
After the break Leinster seemed intent on putting the game beyond their visitors, and they went on the attack from the off. In the 46th minute, after replacement fly-half Ian Madigan cleverly found touch deep in the Scarlets half, Dominic Ryan emerged from a packed ruck to claim a try, but after several replays video referee Dermot Moloney ruled the score out saying it was "inconclusive".
It wasn't long before the hosts made their pressure tell though as they increased the score to 18-5 when from exactly the same position hooker Dundon pushed through the ruck to reach the try-line, the video referee this time giving the score, with Madigan kicking a brilliant conversion.
Madigan, though, joined teammates Goodman and Reid in missing penalties when he skewed his effort in the 57thminute, but Leinster continued to dominate and soon had further reward when No.8 Murphy made a spell of heavy pressure count by charging over the try-line in the 70th minute, converted by Madigan.
As the clock reached 80 minutes Leinster had one final attempt to earn a bonus point, and they succeeded with replacement Cooney charging through the Scarlets defence from close-range, with Madigan again converting.
|Leinster Rugby Score Card|
|Scarlets Score Card|