Caines headed his team level in the 50th minute after earlier making a mistake that handed Tranmere striker Chris Greenacre a 34th minute opener.
It was a close fought encounter that preserved Tranmere's record of only one defeat in League One this season.
The Merseysiders looked neater in their passing and smoother in their attacking play, but there was no denying the steely determination of the home side, who continue to prove a hard nut to crack.
The first half offered little in terms of goalmouth action with Cheltenham enjoying a lot of the ball but finding it hard to do much with it.
In fact, it was hard to see where a goal would come from until 11 minutes before the break when a long kick from John Achterberg caught Caines in two minds and he elected to let the ball bounce over his head.
The proved a bad idea as nippy Tranmere striker Greenacre was able to dart in behind him and beat goalkeeper Shane Higgs with a low shot from a tight angle.
However, Caines made amends only five minutes after the re-start when he rose highest to meet an Andy Lindegaard free-kick with a textbook downward header that bounced in off the goalkeeper's legs.
The game could have gone either way in the closing stages.
Higgs was then forced to save a Steve Jennings shot with his legs, but Cheltenham had chances to drag themselves in front through Damian Spencer, who turned sharply before shooting over the bar, and Paul Connor, who dragged a shot wide after being put clear by John Finnigan.