Right-back Seamus Coleman put Roberto Martinez’s side in the lead after just 18 minutes with a clinical finish on the counter-attack.
QPR came back strongly, though, as substitute Eduardo Vargas fired home the equaliser in the 65th minute.
However, it was Everton who had the last laugh, as Tottenham Hotspur-owned Aaron Lennon struck what proved to be the winner from close range on 77 minutes.
Former QPR winger Sinclair was following the match, and he seemed surprised that Rangers failed to win.
Everton defeated Newcastle United 3-0 at Goodison Park last weekend and made it two wins in a row on Sunday.
Against the Magpies, the Toffees were helped by the dismissal of Newcastle defender Fabio Coloccini, but there can be no doubt that they deserved the three points.
Roberto Martinez’s side had 54% of the possession, took 15 shots of which nine were on target, and earned three corners.
In contrast, Newcastle had 46% of the possession, took 12 shots of which only four were on target, and earned four corners.