Background and Objectives: This paper aims to assess the role of laser therapy in periodontitis through an innovative approach involving computational prediction and advanced modeling performed through network analysis (Gaussian graphical models—GGMs) and structural equations (SEM). Materials and Methods: Forty patients, exhibiting periodontal pockets with a minimum depth of 5 mm, were randomly divided into two groups: a control group and a laser group. Four specific indicators were measured for each tooth, namely periodontal pocket depth (PPD), clinical attachment level (CAL), bleeding on probing (BOP), and plaque index (PI), and the mean of six measured values was recorded at five time markers (baseline, 6 months, 1 year, 2 years, and 4 years). The assessment algorithm included enrollment, measurements, and differential non-surgical periodontal treatment, according to the group allocation. Scaling, root planing, and chlorhexidine 1% were conducted for the control group, and scaling, root planing and erbium, chromium:yttrium-scandium-gallium-garnet (Er,CR:YSGG) laser therapy were conducted for the laser group. Results: The main results highlight that the addition of laser treatment to scaling and root planing led to notable clinical improvements, decreasing the PPD values, reducing the BOP scores, and increasing the CAL. Conclusions: Notable relationships between the specific indicators considered were highlighted by both the GGMs and by SEM, thus confirming their suitability as proxies for the success of periodontal treatment.