The two players were meeting for the second time, with Anderson winning their only other previous encounter in four sets in a Davis Cup World Group playoff tie in 2011. The South African has had a difficult first six months of the season, being hampered by a left knee and right elbow injury, the world number 24 had a 3-8 match record prior to this match.
The top seed makes an ideal start
Both players opened proceedings with very routine service holds to leave the pair locked in at 3-3. The top seed made the crucial breakthrough in the eighth game, breaking the Croat after hitting a down the line backhand winner.
Anderson got himself into a spot of bother down 0-30 when seeking to consolidate the break, but two aces followed by two unreturned first serves secured the hold to help the South African take the set 6-3.
The Croat claims a very competitive second set
Dodig had a rare half-chance to break the top seeds serve in his opening service game in the second set at 30-30 and at deuce but was unable to gain any further ground. The Croat was then under pressure himself at 30-30 but forced his opponent to break down first in an extended rally to reach game point before holding to stay in front.
In the seventh game, Dodig was pushed to deuce on serve but stayed defiant to stay ahead and keep the pressure on the top seed. Both players held serve comprehensively throughout the remainder of the set and the two found themselves in a tiebreak as a result. Dodig earned the first mini-break to take a 4-2 lead at the change of ends after a backhand error from the top seed. A double fault relinquished the Croat's advantage, but that did not deter him from taking the second set as he hit a cross-court forehand winner to finish, winning the tiebreak 7-5.
Anderson secures a crucial win for his confidence
The Croat faced a break point in his opening service game of the final set following an unforced error but managed to save it with an unreturned first serve. Dodig then went on to hold to level at 1-1.
In the fifth game of the final set, Anderson became very animated and frustrated with his game after he squandered a 40-0 lead and a fourth game point. The top seed prevailed with of a roar of "come on" as he walked to the chair with a 3-2 lead intact.
Anderson made the pivotal breakthrough in the eighth game, capitalising on a double fault from the Croat before ripping a return of serve winner to secure the crucial break of serve. The top seed closed out the match on serve with ease, firing down an ace on match point to wrap up a 6-3, 6-7(5), 6-3 win.
The South African goes on to face the 14th seeded Spaniard Fernando Verdasco in the third round.