Allardyce was appointed West Brom manager in December, with the West Midlands club locked in a relegation battle.
The 66-year-old former England manager has cultivated a reputation of steering clubs away from trouble, having guided the likes of Sunderland, Crystal Palace and Everton to safety after coming in at the halfway stage of the season.
Allardyce, who has never been relegated from the Premier League, has lost four of his six top flight games in charge of the Baggies but still got a valuable point against Liverpool at Anfield and won away at Wolverhampton Wanderers.
Guardiola said: "It is not easy to take over a team during the season, but against Wolves, Liverpool, other clubs he got good results.
"Sam Allardyce is a genius to take these teams when everyone believes it is over and get results.
"The results give you an incredible boost, an incredible confidence. What is first - do results make you play good, or do you play good if you get results?
"I think both are connected but we are just at the end of January, so it is just West Brom, trying to analyse them and make a good game to get another victory."
West Brom are still six points away from safety in 19th position while Manchester City can take top spot with victory at the Hawthorns.
