While maintaining a healthy amount of possession and territory, Caversham could not build on its 2-1 halftime lead during a free-flowing second half.
In the 10th minute, referee Brent Best awarded a goal-line hand-ball appeal against Green Island.
The subsequent penalty was successfully converted by Harley Rodeka. Caversham doubled its lead in the 26th minute with some good attacking play down the right flank by Will Smith who hit a teasing cross into the penalty area.
Caversham striker Evan Jones accepted the chance by delivering a highlight-reel diving header.
In the 37th minute, Green Island supporters were comparing Caversham defender Craig Ferguson's perfect no-look pass with household names such as Benji Marshall and Sonny Bill Williams.
Unfortunately for Ferguson, his intended pass to keeper Little went straight to Green Island striker Joel Stevens who stroked the ball into the net from the edge of the box.
At the Caledonian Ground, Dunedin Technical kept its title chase alive with a 3-0 win over University.
In the eighth minute, a classic Aaron Burgess near-post header from a pinpoint Tristan Prattley corner gave Tech the perfect start.
Five minutes later, Victor Da Costa's crossfield pass was inch perfect as team-mate Alistair Rickerby peeled away from his marker, killed the ball with a great first touch and finished with accuracy into the right-hand corner.
An at-times feisty second half resulted in visiting Auckland referee Walker issuing four yellow cards.
Technical killed the game off when it scored its third goal with Mike Flaws providing a deep right-wing cross. Tech striker Rickerby directed his header into the goal to notch his second for the game.
At Bayfield Park, a 41st-minute half volley by Angus Milne enabled second division Fletcher Cup champion Dunedin Technical to edge second-placed Roslyn Wakari 1-0 to retain the Chinese Charity Cup.
• Roslyn Wakari clinched its fifth consecutive women's premier title with a 2 -1 victory over Dunedin Technical at Ellis Park yesterday.
The home side opened the scoring in the 13th minute when a good run from Monique Francois ended with a sharp byline cut-back to team-mate Una Madden who tapped home from close range.
Roslyn doubled the score in the 36th minute when Sam Muirhead converted a second-chance penalty after Una Madden skied the first attempt. Match officials signalled a retake after Tech keeper Tess Nicol was adjudged to have moved off her line early.
In a game in which many observers thought Technical played the better football, the visiting team was rewarded with a second-half penalty which Chelsea Whittaker smashed home to narrow the margin.
By Wilson James.