Ward - who reached the semi-finals here at Queen's last summer, beating Stanislas Wawrinka and 2010 champion Sam Querrey en route - raised hopes of another upset when he took the first set off the world number 30 on centre court in the duo's rain-delayed match.
But Ward's serve was poor in the final two sets and Anderson's power proved too much, allowing the South African to ease to a relatively comfortable 4-6 6-3 6-4 win.
Anderson set the tone for the opening few minutes of the match by sending down a flurry of powerful serves to hold to love in the first game, but Ward held steady and rarely looked nervous after.
The 25-year-old double-faulted in the fourth game but he hit back with two powerful aces to level at 2-2.
Indeed Ward was making his opponent work hard for his points, forcing the tall South African across the court with some well-placed shots from the baseline.
Anderson started to look worried by Ward's play and carelessly misplaced two forehands to give his opponent a break point. And Ward did not waste it, forcing Anderson back on to the baseline where he pushed another forehand wide.
The Briton held his nerve to take the second of two set points in the following game, the winner coming after Anderson spooned a backhand long.
Ward's first-serve percentage dropped in the second set, however, and Anderson capitalised, breaking the Englishman in the fourth game when he found the net.
Two double-faults from Anderson gave Ward an immediate chance to break back but Anderson showed why he is rated so highly by powering down three unreturnable serves to deny the home favourite.
Ward, now playing nervously, handed Anderson three set points in the seventh game but he denied the South African on all three occasions.
Anderson already had the crucial break, though, and he held his serve to level the match.
Ward won his first service game in the third set but then wobbled in the third game, double-faulting to give Anderson three break points.
The big South African hammered down a punishing forehand to break and kept his composure to close out the final set and send Ward out.