Adams, who was forced to watch the game from the sidelines while serving a one-match touchline ban for five yellow cards, saw a mixture of yet more bad luck and more poor defending prove costly.
The Shrimps, who had shown plenty of spirit, could not find their way back into the game after conceding either side of the break.
The game came to life when the visitors took a fortunate 44th minute lead as Liam Sercombe’s speculative 25-yard effort took a wicked deflection off Jacob Bedeau to loop over Trevor Carson and into the net.
Cheltenham then added a second a minute after the break after the Shrimps failed to clear their lines from a long throw.
Elliot Bonds was allowed to drill in a low shot which was well saved by Carson, only for the ball to fall perfectly for Callum Wright to score from three yards out.
Morecambe hit back quickly as Shane McLoughlin, Anthony O’Connor and Cole Stockton all saw goalbound shots blocked before Greg Leigh made it 2-1 on 52 minutes with a close-range finish from Stockton’s cross.
They were then denied a clear penalty when Dylan Connolly was upended by Charlie Raglan – only for the referee to wave away their appeals.
Lewis Freestone also seemed to trip Connolly inside the box but another negative response from the man in the middle added to the Shrimps’ frustrations.
The game swung from end to end, Carson making a stunning stop to tip away Matty Blair’s close-range effort before Robins’ keeper Owen Evans saved smartly from Stockton.
However, Morecambe’s hopes of a comeback were denied 10 minutes from time with another close-range finish.
Alfie May tucked away his 21st goal of the season when he was left unmarked at the far post after Sercombe had scuffed his shot.
Morecambe: Carson, O’Connor, Bedeau, Gibson (Ayunga 78), McLoughlin, McCalmont (Obika 53), Diagouraga, Leigh, Phillips, Connolly, Stockton. Subs not used: Smith, Gnahoua, Mensah, Cooney, Fane.
Cheltenham Town: Evans, Long, Raglan, Boyle, Blair, Sercombe, Bonds (Colkett 60), Wright, B Williams (Freestone 66), May, A Williams (Lloyd 85). Subs not used: Flinders, Ramsey, Pollock, Chapman.
Referee: Andrew Kitchen.