Meeting in Merseyside for the first time in seven years it was a lively encounter with chances for both sides in the opening 45 minutes.
Jordan Green forced a good save early on whilst the hosts’ top scorer James Norwood failed to find the back of the net with a hat-trick of chances.
As the break approached, the visitors spurned a glorious opportunity when Yoann Arquin failed to convert from close range to see it stay goalless at the halfway stage.
In a cagier affair after the restart chances were restricted as an opening goal remained elusive.
Stuart Nelson continued his theme of denying Norwood early on before the game petered out to see both sides have to settle for a point.
For the final match of the year, Darren Way made one change to the side that narrowly lost out to Exeter City on Boxing Day.
Fresh from signing a contract extension until the end of the 2018/19 season, Arquin was rewarded with a starting spot in place of Rhys Browne who dropped to the bench.
With no fresh injury concerns the matchday 18 remained the same with Omar Sowunmi (ankle), James Bailey (knee), Alex Pattison (back), Gabby Rogers (ankle), Wes McDonald (hamstring) and Diallang Jaiyesimi (knee) unavailable.
Bathed in late December sunshine both sides kicked off with displays of attacking intent as Tom James had a free-kick from long range comfortably gathered by Scott Davies inside the opening five minutes.
With the visitors enjoying plenty of early territory the Super White Army hit back with a wave of pressure themselves.
A sweeping counter-attack ended with James Norwood dragging an effort wide, quickly following that strike up with a low drive which forced Nelson into a save after seven minutes.
Remaining a fast flowing affair the Glovers were quickly in action at the other end when Carl Dickinson’s switch found Green in space, with the winger scampering past Liam Ridehalgh before forcing Scott Davies into a smart one-handed save from the angle.
Evolving into an an interesting tactical battle with Tranmere’s 3-5-2 against Town’s 4-4-2, those inside Prenton Park had to wait until almost the half-hour mark for the game’s next opportunity.
Jake Caprice’s cross from the right found its way all across the box to Cole Stockton, whose first-time strike had to be parried away by Nelson.
Finding a bit of rhythm going forward Micky Mellon’s side had Town’s keeper in action once again soon after, this time to keep out Norwood’s low drive with his feet as the 18-goal man was kept at bay before the break.
With just four minutes left before half-time Rovers were saved their blushes by some wayward Yeovil finishing.
Caught in possession in their own box, Green was afforded the chance to pick out an unmarked Arquin in the middle but his scuffed shot from just six yards was straight at Davies to provide the Merseyside outfit with a huge let off.
Returning the generosity after the restart, Tranmere were almost gifted the opener inside 60 seconds.
A low cross into the box was fumbled by Nelson to allow Stockton a shot at goal, but Adel Gafaiti spotted the potential danger to get back on the line and head clear.
Buoyed by that early excitement the home crowd cranked up the decibel levels inside Prenton Park in the second half and watched on as Nelson once again denied Norwood.
The striker got a strong head to Jay Harris’ deep free-kick to force the stopper into palming the ball behind for a corner.
Now into the final 20 minutes the importance of the first goal grew, as the Super White Army made a tactical switch to match Yeovil’s 4-4-2 for the closing stages.
But it was the visitors who almost benefited from the removal of Tranmere’s extra defender when Francois Zoko raced through with support from Alex Fisher.
Spotting the run of his teammate he slipped a pass into the box, but a charging Davies did enough to get something on Fisher’s attempted chip.
In the closing stages there was time for Nelson to once again deny Norwood as he had all game, diving down low to his right to get two hands to the striker’s header to confirm a point would join him on the journey home to Somerset.
Tranmere Rovers: Davies; Ellis, McNulty, Sutton (Mullin 69′); Caprice, McCullough, Harris, Ridehalgh; Jennings; Norwood, Stockton (Smith 61′).
Bookings: Ridehalgh 34′
Subs not used: George, Bakayogo, Buxton, Gilmour, Cole.
Yeovil Town: Nelson; James, Warren, Gafaiti, Dickinson; Green, Santos, D’Almeida, Arquin; Zoko (Olomola 83′), Fisher.
Bookings: Dickinson 38′
Subs not used: Baxter, Donnellan, Mugabi, Gray, Browne, Arnold.