Full-back Martin Kelly also played in the match as he steps up his recovery from a ruptured anterior cruciate ligament injury that has kept him out for 10 months.
Uruguayan striker Suarez appears to have been welcomed back into the first-team fold after a brief period of exile after he publically expressed his desire to leave the club.
Suarez went public with his grievance that he believed the Reds had reneged on a deal struck last summer which allowed him to leave for a Champions League club - and that a second bid of £40million plus £1 by Arsenal should have triggered his departure.
Liverpool have always maintained there was no release clause as such, only a requirement to notify the player and begin negotiations should they wish.
Suarez has three games left of the 10-match ban he received near the end of last season for biting Chelsea's Branislav Ivanovic.
He will miss the next three Premier League clashes against Manchester United, Swansea City and Southampton but will be eligible for Liverpool's as yet to be determined third round tie in the League Cup.