Purpose: To explore the clinical evidence available on mindful organizing (MO) that will improve teamwork for positioning and managing central venous catheters in patients admitted to neonatal intensive care and other pediatric intensive care units to decrease central-line-associated and catheter-related bloodstream infections (CLABSI and CRBSI). Methods: We searched several databases (PubMed, Embase, CINAHL, CENTRAL, SCOPUS, and Web of Science) up to June 2018. We included studies investigating the effectiveness of MO teamwork in reducing CLABSI and CRBSI. The systematic review followed the PRISMA guidelines. We used validated appraisal checklists to assess quality. Results: Seven studies were included: only one was a non-randomized case-controlled trial (CCT). All the others had a pre-post intervention design, one a time-series design and one an interrupted time-series design. The methodological heterogeneity precluded a meta-analysis. Despite the low certainty of evidence with the Grading of Recommendations Assessment, Development and Evaluation (GRADE) system, three studies including thousands of participants provided numerical data for calculating risk ratios (RR) and 95% confidence intervals (CI) comparing MO with no intervention for decreasing the CLABSI rate in neonatal and pediatric ICUs. The one CCT disclosed no significant difference in the CLABSI rate decrease between groups (RR = 0.96; 95%CI 0.47–1.97). Nor did the pre- and post-intervention interrupted time-series design disclose a significant decrease (RR = 0.80; 95%CI 0.36 1.77). In the study using a before-after study design, the GRADE system found that the CLABSI rate decrease differed significantly in favor of post-intervention (RR = 0.13; 95%CI 0.03 0.57; p = 0.007). Conclusions: Despite the decreased CLABSI rate, the available evidence is low in quality. To reduce the unduly high CLABSI rates in neonatal and pediatric intensive care settings, custom-designed clinical trials should further define the clinical efficacy of MO to include it in care bundles as a new international standard.