Despite being given an early advantage by Fernando Torres' third goal in four days, the visitors lost their grip on the game midway through the first half and never regained it.
Wigan equalised through Rodallega in the 52nd minute and finished the better side as the Merseysiders appeared to feel the exertions of beating Premier League leaders Chelsea on Sunday.
That will be a concern to manager Hodgson, who has complained about the depth of quality in his squad, with a trip to Stoke next up on Saturday.
The draw meant Liverpool missed the chance to move into the top five - a scenario which seemed a distant prospect just a few weeks ago with the Reds mired in the relegation zone until they put together three league wins to add to a victory in Europe.
It must also have annoyed Hodgson because, as they did against Chelsea, his side began strongly with Sunday's man of the match Lucas Leiva unleashing a 25-yard strike which Ali Al Habsi just managed to tip over.
The next time the visitors attacked the goalkeeper was given no chance by a clinical Torres.
An unusual statistic for this season is that all Liverpool's league goals, apart from their opening match against Arsenal, have either been scored or provided by Steven Gerrard and Torres.
The Reds' star duo demonstrated why their partnership is so successful in the seventh minute when Gerrard was given far too much time to carry the ball through midfield.
His perfectly-weighted 30-yard pass allowed Torres to outpace Gary Caldwell and fire across Al Habsi into the far corner of the goal.
It was the 26-year-old's first away goal since March 21 and, considering his prolific record, only the 17th in 41 matches outside Anfield.
The simplicity of that strike was contrasted by their next move, which saw Gerrard, Torres and Dirk Kuyt combine before the captain volleyed over from the Dutchman's header.
Torres was looking at his dangerous best and when Antolin Alcaraz stumbled he was clean through only for referee Peter Walton to pull play back for a non-existent foul.
Charles N'Zogbia looked Wigan's best outlet and he thought he had equalised in the 33rd minute when he seized on Lucas' weak pass and played a one-two with Rodallega to tap home but his team-mate had already been flagged offside.
A Ronnie Stam pass intended for Rodallega at the near post rolled agonisingly wide of the far upright as Wigan finished the half on the up.
Raul Meireles was replaced by Jonjo Shelvey for the start of the second half and the teenager's first contribution was to give the ball away to Rodallega but his forward pass to N'Zogbia was too strong.
The Colombian was not so wasteful moments later when Jose Reina could only palm Stam's low cross into his path and he gratefully fired home left-footed.
Wigan sensed their chance as Liverpool's play became increasingly ragged and Martinez sent on young forward Victor Moses for Jordi Gomez.
Kuyt's strike from Shelvey's deflected shot was half-saved by Al Habsi before it crossed the line but the Holland international had come back from an offside position and it was ruled out.
It was a brief rally as Stam again found room down the right to cross and Martin Kelly had to hack away at the far post under pressure from Tom Cleverley.
Gerrard's shot 10 minutes from time crashed down off the crossbar but not over the line with Al Habsi beaten as the game became end-to-end.
But it was Liverpool who were grateful for the final whistle as Mohamed Diame and N'Zogbia both forced low saves out of Reina.
The result may prove to only be a blip in Liverpool's recovery but Hodgson cannot allow his side to lose any momentum having built up so much confidence over the last three weeks.
Wigan may ultimately have been disappointed with a point, having won the corresponding fixture last season and finished so strongly, but it at least avoided a third successive league defeat.