Despite a 27th-minute straight red card for Jermain Defoe, the Dutch midfielder scored either side of that to take his tally to double figures for the season.
Although Marc Albrighton pulled one back eight minutes from time with a cross that curled into the net, it was not enough to spare the home side, with Redknapp unbeaten in his last 10 Barclays Premier League games as a manager against Villa.
Villa appealed for a penalty in the ninth minute when Emile Heskey was felled by Heurelho Gomes, but it was such a tight call it was no wonder referee Martin Atkinson was unmoved.
An effort by Younes Kaboul was ruled out by an assistant referee as he deemed a pull back from Alan Hutton had crossed the deadball line, although replays suggested otherwise.
Source: PA
Source: PA