The former Newcastle United striker got the hosts off to the perfect start in the third minute after being found by Marc Burch.
Rave Green continued to dominate thereafter, with Martins nearly doubling their advantage in the eighth minute.
However, they had to wait until seven minutes before the break to extend their lead, with Neagle powering home from DeAndre Yedlin's cross from the right.
Real goalkeeper Nick Rimando pulled off a fine save to deny Neagle a second in the 54th minute.
The 34-year-old was in fine form to limit the damage to just two goals, which means that Jason Kreis and his side surrender top spot.