The former Gillingham midfielder fired home the winner in first-half stoppage time after goalkeeper Shane Higgs failed to hold Neil Harris' effort - leaving Spiller all alone to slot home into an empty net.
The hosts should have extended their lead in the second half with former Leyton Orient striker Gary Alexander wasting two glorious opportunities, while Higgs made amends for his earlier error with an impressive stop from the striker.
But despite dominating the game, Millwall were forced on the back foot in the closing stages as John Ward's men threatened to find an equaliser.
And Cheltenham came within a whisker of rescuing a point when Shane Duff's towering header ricocheted off the woodwork and away to safety.
Milwall should have taken an early lead through Ben May after just two minutes, but the striker failed to connect with Alan Dunne's header after Dave Brammer had swept the ball into the Cheltenham penalty area.
The home side continued to dominate possession but failed to turn their territory into goals despite finding Cheltenham in generous mood in terms of giving possession away.
But to their credit, Cheltenham improved markedly after the break and forced their way back into the game but couldn't find that elusive goal.
Duff came closest to restoring parity in the 82nd minute, but his header rebounded to safety off the woodwork as Millwall hung on for all three points.