Spillane prodded home Rossi Jarvis' corner seven minutes into the second half to boost the Hatters' hopes of beating the drop.
But Carlton fired home an excellent leveller five minutes later from Craig Stanley's corner to leave matters all square.
Luton started at breakneck pace and were almost ahead inside a minute as Kevin Gallen accelerated into the box and back-heeled into the path of Paul McVeigh, but the former Norwich man's side-foot effort lacked the necessary power and was held by Barry Roche.
Five minutes later, Jarvis almost set Chris Martin free down the middle only for Fraser McLachlan to produce a timely saving tackle.
Martin was involved again in the 11th minute as he teed up Asa Hall to fire a low shot just past the post.
Morecambe woke up and missed a great opportunity in the 17th minute when Carlton lost his marker in the box only to head wide from 10 yards after Stanley's free-kick.
A Hatters free-kick at the other end in the 27th minute saw Jarvis touch the ball to Keith Keane, who fired in a low drive from 18 yards that was held by Roche.
Morecambe ended the half in more positive mode and Carlton went close again when his glancing header from Stanley's corner had to be cleared off the line by Jake Howells in the 32nd minute.
Luton saw Keane replaced at half-time by Ed Asafu-Adjaye, but the loss of their skipper had no immediate affect as the hosts took the lead in the 52nd minute.
Jarvis took Luton's first corner of the game and Spillane stole in to prod home his fourth of the season from eight yards.
The lead was short-lived, however, as five minutes later a Morecambe corner led to the leveller as Stanley's flag-kick was powerfully volleyed home by Carlton from 15 yards.
The game degenerated into a tense midfield battle with home full-back Howells' speculative 25-yarder the only effort of note.
In the last minute, Spillane came close to a winner when he headed Jarvis' free-kick wide from 10 yards.