The Pilgrims battled their way to a 1-1 draw at The Jakemans Stadium and needed Davies' 36th minute penalty to restore parity following Colby Bishop's third minute opener for the Brakes.
Visiting keeper Tony Breeden made superb saves to deny Ryan Qualter, Gavin Allott and Nicky Walker, while Jay Rollins struck the inside of the post for Craig Elliott's side as they endured frustration in attempts to secure all three points.
United had opened brightly, forcing two early corners and Allott miskicking in front of goal following Rollins’ cutback from the right.
The third corner of the game went the way of Leamington and from Jordan Murphy’s delivery, BISHOP guided home a neat header at the near post.
United upped the ante and Qualter headed two efforts off target before being denied by a flying Breeden save following Davies’ corner.
Boston were awarded a penalty when James Bowen swiped Max Wright’s feet from underneath him and DAVIES sailed home his fourth spot-kick in five matches.
Rollins headed wide following Jonathan Wafula’s cross from the left while Breeden excelled to keep out Allott’s downward header which seemed destined for the bottom corner. Rollins, meanwhile, had an effort ruled out for offside.
A big moment unfolded in the 66th minute when Rollins burst into the area, only to see his angled effort bounce back off the inside of the far post, along the line and into the grateful clutches of Breeden.
United looked the likelier to snatch a winner and Breeden produced his best save yet to keep out Walker’s stoppage time bullet, before tipping a Lewis Gibbens header over the bar at the death.
Boston (4-4-2): George Willis; Ben Davies, Ryan Qualter, Lewis Gibbens, Ashley Jackson; Max Wright, Brad Abbott (Spencer Harris 67), Andi Thanoj, Jonathan Wafula (Nicky Walker 78); Gavin Allott, Jay Rollins (Jordan Slew 86). Subs (not used): Callum Chettle, Andre Johnson.
Leamington (4-2-3-1): Tony Breeden; Junior English, James Mace, Jack Lane, James Bowen; Jack Edwards, Callum Gittings; Kieran Dunbar (Connor Taylor 8), Jordan Murphy, Ahmed Obeng; Colby Bishop. Subs (not used): Tom James, Martyn Naylor, Ben Newey.
Referee: Aaron Jackson.
Attendance: 885 (25 visitors).