Day denied Paul Heffernan an opening day hat-trick with a trio of fine saves as Rovers piled on the pressure without finding the net.
Despite the scoreline it was an entertaining match, with both sides producing some decent football in the humid conditions.
Rovers started brightest and James Coppinger hit a dipping 25-yarder just over the bar in the ninth minute, before Martin Woods had another well-struck shot deflected moments later.
It was mostly Doncaster, but Millwall's danger man, tall striker Ben May, headed down for Neil Harris to have a shot on the turn saved by Neil Sullivan's legs.
Day gave a hint of what was to come when he dived full length to tip away a cracking effort from Heffernan in the 17th minute and then saved a swerving shot from Mark Wilson a couple of minutes later.
A volley from Millwall striker Gary Alexander lacked pace and was comfortably saved by Sullivan in the 20th minute, before Rovers resumed on the attack with Heffernan firing just wide in the 35th minute.
May headed a good chance wide following a free-kick just before the interval, but it was Doncaster who continued to call the tune after the interval.
Heffernan fired inches wide from the edge of the box and James Hayter was foiled by Day's reflexes in the 55th minute.
James Coppinger and Heffernan went close in quick succession for Doncaster before Day came to the rescue again to save a header from Mark McCammon in the 79th minute.
May had a shot on the turn saved by Sullivan seven minutes from time, but overall Doncaster looked more impressive and should have won the match.