Abraham, who scored 26 times on loan to help Villa to promotion last season, returned from a hip injury on Wednesday and claimed his 11th Premier League goal of a brilliant breakthrough campaign to put Chelsea ahead after 24 minutes.
Trezeguet rounded off a fine move in somewhat comedic fashion to pull Villa level before the break, but a wonderful Mason Mount volley - from Abraham's chested lay-off - restored the home side's lead early in the second half.
Chelsea was unable to claim the additional goals as a host of further chances went begging, but manager Frank Lampard could still be happy with a much-needed three points in the wake of successive losses to Manchester City and West Ham, his only real concern being the sight of Abraham limping off in the closing minutes.
Villa, sitting perilously close to the relegation zone, were far too passive early on and could have few complaints when they fell behind. Abraham, absent for his side's below-par display against West Ham, was left unmarked to head home a Reece James cross, having been played onside by Ahmed El Mohamady.
Chelsea struggled to build on its breakthrough, though, and it was punished shortly before the interval. A flowing Villa move ended with El Mohamady delivering a teasing ball, which Trezeguet fortuitously bundled into the net after initially heading down on to his own legs.
It took less than three minutes of the second half for Chelsea to retake the lead, Mount showing superb technique with a volley after Willian's cross had been chested down by Abraham.
The hosts could have scored several more as Willian continued to run Villa ragged and the Brazilian was only denied a goal of his own when Tom Heaton - Villa's best player - made a spectacular save to tip a free-kick onto his left-hand post.