The pair lie second and third, respectively, behind table topping Langley Manor in the log, St Cross currently trailing Oaks by 11 points.
While Langley Manor were washed out against Waterlooville, their two challengers enhanced their claims – Fair Oak winning by 59 runs at relegated Ryde and St Cross Symondians making it four wins in a row by beating their Havant counterparts by five wickets.
Rufus Bullough, pictured, was the hero of Oaks win on the island, hitting a maiden Premier League 113 not out.
With Hampshire Under-14s starlet Fletcha Middleton (50) providing invaluable support, the former Peter Symonds College student hauled Fair Oak out of the mire after Matt Webb (3-26) had struck early blows with the new ball.
Gradually the pair turned the tide, with a near century stand which largely set up Oaks’ 239-8.
Bullough, who has been playing for Old Elizabethans to coincide with his drama studies at Worcester University, went on to smack three sixes and 13 fours in a career best knock.
Initially, Ryde made a decent fist of chasing down the target, with Ben Wadmore (42), Sam Rockey (28) and Cameron Mitchell (26) taking their response to 112-1.
But Ryde’s reply fell apart against off-spinner Rhys Oxley, whose 5-19 return triggered a collapse which saw the last nine wickets fall for 59 runs and the already doomed island team sink to 171 all out.
Steve Mitchell (3-24) plunged Havant II into trouble at 14-4 and later 42-7 before Graham Burns (38) and Jack Davies (24) rallied to lift the final total to 119 against St Cross Symondians II at the Green Jackets.
Matt Howarth (3-40) and Harry Trussler (2-18) cut through the lower order before a sound start by Paul Hawkins (45) and Graham Barrett (25) laid the foundations for a home five-wicket win