The U's were looking for a second Sky Bet Football League scalp this week after knocking out Bury on Tuesday and started brightly, but were eventually kept at arm's length by their League One opponents.
Both sides came close to an early breakthrough as Kwesi Appiah had a shot blocked by what he thought was an arm before Baxter's header was saved by keeper Chris Maxwell.
Baxter then gave the Blades the lead after 12 minutes when he met Ryan Flynn's low cross with a crisp, first-time finish that gave Maxwell no chance.
Cambridge were almost level within two minutes when the Blades goalkeeper George Long produced a good block to deny Adam Cunnington.
The U's hero from the last round, Luke Berry, then wasted a golden chance to level early in the second half as he ballooned a free header from Harrison Dunk's corner over.
And he was made to regret that miss as Blades substitute Murphy doubled his side's lead when he was allowed to cut inside from the left before shooting inside the near post.