Spurs fans had started to turn on Frank after a run of five defeats in eight left them 14th in the Premier League on Christmas Day.
While there had been no suggestions internally that Frank’s job was under immediate threat, Tottenham needed to return to winning ways and Gray’s 42nd-minute header settled the contest between the current FA Cup and Europa League holders.
It moved Spurs up to 11th but crucially they are only four points off fifth-placed Chelsea ahead of Frank’s return to old club Brentford on Wednesday.
Oliver Glasner watched his weary Palace team lose a third consecutive league game to further highlight the need for January reinforcements.
Both clubs had celebrated eagerly-awaited cup wins in May but Spurs were without one of their heroes from Bilbao with Cristian Romero suspended.
Kevin Danso replaced Romero and received a late Christmas present in the shape of a yellow card from referee Jarred Gillett after five minutes as Palace made the early running.
Chances remained limited, though, and Tottenham thought they had taken the lead in the 17th minute through Richarlison only for their celebrations to be cut short after Lucas Bergvall was deemed offside in the build-up.
Jean-Philippe Mateta signalled his intentions with an effort dragged wide from 20 yards soon after before a short free-kick routine created another chance for Palace’s number nine but he nodded over from Maxence Lacroix’s header.
Justin Devenny and Adam Wharton tested Guglielmo Vicario with tame efforts before Will Hughes curled wide after a slick move by the hosts.
It appeared a matter of time before Palace broke the deadlock but Spurs struck against the run of play in the 42nd minute.
After Randal Kolo Muani’s blocked shot forced a corner, Pedro Porro’s delivery to the back post was kept alive by Kolo Muani and then flicked on by Richarlison for Gray to head home from close-range to open his account for Tottenham.
Spurs’ slender half-time lead was immediately under threat as stand-in away captain Micky van de Ven blocked Yeremy Pino’s volley before an even better opportunity was created.
Pino produced a sumptuous outside-of-the-boot cross which was knocked down by Nathaniel Clyne but Devenny fired over on the turn.
Glasner turned to his bench with Eddie Nketiah introduced and another Palace chance was squandered with 20 minutes left when Jefferson Lerma teed up Lacroix but he sent his header wide.
Five minutes later and Tottenham had the ball in the net again through Richarlison after a wonderful Mohammed Kudus cross only for VAR to deny the visitors again as the Brazil forward was marginally offside.
Palace captain Marc Guehi went close next after he headed over but no grand finale occurred as Spurs defended resolutely, with substitute Wilson Odobert unlucky to hit the inside of the post from range before Dean Henderson denied Rodrigo Bentancur as it finished 1-0.