This isn't true (with the exception of the Patriots). As with just about any statistic over the last 20 years, the Patriots are the greatest outlier/exception in sports history. Records in close games from 2014-2019:
Patriots - 21-9 (High win % = 100% this year so far, low = 60%, Median = 71%, 21% above expected 50%)
Steelers - 29-20 (High win % = 80%, low = 50%, Median = 56% --> 6% above expected)
Seahawks - 26-22 (High win % = 88%, low = 29%, Median = 50% --> 0% above expected)
Cowboys - 23-17 (High win % = 80%, low = 0% this year so far, Median = 61% --> 11% above expected)
Record in close games is extremely random year-over-year but over time usually ends up around 50%, which is the very definition of luck-based (with the exception of the Patriots as usual).