The basement battlers pushed hard from the start at Horntye Park but couldn't find a way past a tight defence marshalled by Phil Carrington and young Warrior Matt Stevens.
Teenage winger Tom Giles cracked the post on 10 minutes after collecting Sol Buckner's defence splitting pass.
But Saxons had to wait until the 22nd minute to open the scoring.
Carrington smashed home after the visitor's keeper parried Buckner's short corner shot.
The second half saw Saxons crank up the pressure and we're rewarded on 42 minutes when Paul Merison's piledriver into the D was fumbled by the keeper and trickled under his legs for an own goal.
St Francis held firm until the hour when Buckner flicked a short corner shot high past the keeper for his ninth of the campaign.
The visitors then grabbed a deserved consolation from a short corner.
Buckner said: "St Francis may have been bottom of the league but they never gave up and showed exemplary courage and spirit.
"We played some attractive stuff again and made our short corners pay off for once. It was another great advert for hockey in our division."
Saxons welcome Eastbourne V to Horntye Park on Saturday for a 1.30pm push back
Man-of-match: Carrington
Team: Heath, Pickard, Carrington, Roberts, Kellett, Waters, Stevens, Buckner, Ball, Merison, Giles, Lovell, Cornelius, Rand,