The incident came midway through the second half as Kiernan Dewsbury-Hall sized up a free-kick, as Martinez collided with Jarrad Branthwaite at speed.
Both parties required treatment, and Martinez left the pitch on a stretcher wearing a neck brace and receiving oxygen before being hospitalised. The highly-rated Mike Penders replaced him, making his Premier League debut.
Beyond the injury, it was a positive afternoon for Xabi Alonso’s men. Neto’s second-half brace secured back-to-back league wins for the first time since the second week of the campaign. The clean sheet, meanwhile, was their first since January 17 of this year, nixing an ignominious run of 23 matches without one. For Everton, it was a first defeat of the season.
An initially pedestrian first half sparked into life when Harrison Armstrong threw himself into a full-throated tackle on Josh Acheampong, earning a booking for his troubles but also getting the home fans on their feet.
There was plenty more animosity. Tempers flared when James Tarkowski shoved Moises Caicedo to the ground and was confronted by Morgan Rogers, who later left James Garner in a heap after an aggressive fifty-fifty.
It was not a half without chances. Thierno Barry should have scored when he nodded an early header into Emi Martinez’s arms, shortly after the Argentine tipped a bouncing Jack Grealish effort over. Caciedo left the woodwork vibrating with a clattering volley.
The deadlock would not hold for long after the break, though. The Londoners took the kickoff and immediately marauded down the left flank, and Jorrel Hato’s cross was coolly slotted home by Pedro Neto.
Rogers then seemed set to double the Blues’ advantage ten minutes later as he latched onto Neto’s cross, but a perfectly timed block from Merlin Rohl denied him.
Chelsea pushed on and looked to suffocate their hosts, who were not much improved by the introduction of Tyrique George to face his former club just before the hour mark.
Any semblance of momentum in the tie was dashed, however, when Martinez went down with a serious injury after a concerning clash with Jarrad Branthwaite, which left both men requiring treatment. The Argentine shot-stopper received oxygen and, after a ten-minute stoppage, was stretchered off wearing a neck brace before being rushed to hospital.