Union keeper Mohamed Khalaf needlessly rushed out of his goal to allow Gaafar notch the winner with one minute remaining.
Telecom Egypt, who struggled to guarantee their top-flight status last season, gave new coach Helmi Toulan a winning debut.
Chances were few and far between in an uninspiring first-half.
Telecom Egypt had the better possession and came close to breaking the deadlock in the 26th minute.
Wael Riad's deflected cross found towering striker Magdi Abdul-Atti, who headed astonishingly wide with the goal gaping.
Union forward Essam Abdul-Atti tried his luck from distance on two occasions but his efforts narrowly missed the target.
The second half was no different than the first one as neither side was able to create goalscoring opportunities.
Khalaf blocked a curling free-kick from Telecom Egypt defender Wael Al-Qabani midway through the second period.
However, he was to blame for the match's decider one minute from time.
Gaafar controlled a deft through pass on the edge of the area, and spotted Khalaf coming out of his goal.
He then sent a low shot that went between the legs of Khalaf and into the back of the net to give Telecom Egypt a winning start.