In the process, star playmaker Benji Marshall overhauled former captain Brett Hodgson's club record of 786 points to become the joint venture club's highest pointscorer with 797.
The Tigers move to sixth on the ladder after a sixth straight win and a top four finish is a real possibility with games against cellar dwellers Gold Coast and Cronulla to come.
Parramatta are dead last after Gold Coast beat Canberra on Saturday night and their round 26 clash with the Titans, who are one point ahead, shapes as a "grand final" to avoid the wooden spoon.
As well as Ayshford, Matt Utai and Marshall scored tries for the Tigers, with Marshall adding five from six with the boot and Robbie Farah a field goal.
For Parramatta, Chris Hicks and Ben Smith bagged four-pointers, while Luke Burt kicked two from two.
The Tigers looked to have increased their halftime lead three minutes after the break but Utai was unable to ground the ball over the line.
Parramatta gave themselves some hope when Jarryd Hayne sent winger Hicks over out wide four minutes later, Burt's conversion making it 16-6.
And the Eels were back in it at 16-12 when Smith grabbed the scraps of a Hayne bomb and dived over.
Ayshford's try in the 59th minute made it 22-12 and a 67th minute Marshall penalty goal took the Tigers out to two converted tries.
Farah added a 76th minute field goal and Ryan a 79th minute try from a superb Marshall cut-out ball.
Earlier, after Parramatta had ruined their early territorial advantage with errors, the Tigers scored with their first foray into the Eels' danger zone.
Robert Lui, who a report on Sunday linked with a move to North Queensland, beat three defenders and popped an overhead pass for Ayshford to score in the 10th minute and it was 4-0.
Quick hands from Marshall and Chris Heighington sent Utai over in the 22nd before Marshall capitalised on a Casey McGuire error, dummying, stepping and swerving his way to the Tigers' record and a 16-0 lead.
WESTS TIGERS 31 (B Ayshford 2 B Marshall B Ryan M Utai tries B Marshall 5 goals R Farah field goal) bt PARRAMATTA 12 (C Hicks B Smith tries L Burt 2 goals) at Sydney Football Stadium. Referee: Jared Maxwell, Chris James. Crowd: 18,626.
- AAP