Saunders scrambled home the opener three minutes before the end of an entertaining first half and John Sutton claimed his 12th goal of the season moments later.
The goals were reward for an enterprising display and Motherwell came close to adding to their lead in a comfortable second half.
Four wins from their five previous home games had given Hearts hope of sneaking into the European places but Motherwell showed no sings of losing confidence following four consecutive defeats. They leapfrogged Hibernian into fourth place in the Scottish Premier League and extended their lead over their opponents to seven points.
Hearts were on the back foot from the early stages with Jamie MacDonald pushing away Steve Jennings' powerful, deflected strike.
Lukas Jutkiewicz then saw two 20-yard drives fall just past the post, the first helped wide by MacDonald's touch.
Hearts were soon lifted by an enterprising run from David Templeton, whose 20-yard strike was spilled by Michael Fraser. But the goalkeeper did enough to stop David Obua netting the rebound and Gary Glen fired the Ugandan's cutback over the bar from 10 yards.
Motherwell were soon back on the attack and the lively Giles Coke, who was breaking into promising positions from central midfield, saw a 20-yard strike deflect inches wide.
Lee Wallace got Hearts going with a surging run but Obua was flagged offside as he failed to turn the left-back's shot home, and Jutkiewicz soon volleyed over from Jim O'Brien's head-down after a flowing move.
The chances continued to fall at both ends and Glen blazed over from 18 yards following another good run from Wallace. Fraser held Suso Santana's volley after excellent wing play from Templeton and MacDonald made a flying save from Coke's first-time effort after a low cross from O'Brien.
Craig Thomson saved Hearts with a covering tackle after Tom Hateley's through-ball had played Jutkiewicz in but Motherwell went ahead from the resulting corner when Saunders forced the ball home after his header from Stevie Hammell's delivery had been blocked on the line.
Well doubled their lead in injury time with Sutton scoring as the striker and Zaliukas challenged for Tom Hateley's inswinging free-kick.
Glen and Michael Stewart had been restored to the Hearts starting line-up but they made way at half-time with Calum Elliot and Black coming on and, with little early indication of a comeback, Jim Jefferies made his final change in the 54th minute when he replaced Obua with Ryan Stevenson up front.
Suso headed high over after a long throw but there was no sustained pressure from the hosts and MacDonald held Coke's volley after a rehearsed set-piece. Hearts had a huge let-off on the hour mark after a poor decision from referee Brian Winter to haul back O'Brien as the winger charged clear on goal.
An attempted flick from last defender Zaliukas hit O'Brien in the face but, with his better-placed assistant playing on, Winter penalised the winger for handball.
The decision proved to be of little consequence as Hearts failed to seriously threaten the visitors' goal with Fraser making comfortable saves from long-range efforts by Stevenson and Thomson. Motherwell should have added to their lead after O'Brien played Sutton in but MacDonald came off his line to block and Zaliukas cleared Jamie Murphy's follow-up off the line.
Murphy later brushed off Zaliukas to collect fellow substitute Chris Humphrey's ball over the top but MacDonald blocked at point-blank range.