Wayne Rooney scored his 43rd international goal as England beat Estonia 1-0 to preserve their perfect Euro 2016 qualifying record on Sunday while his former boss Fabio Capello saw Russia held 1-1 by Moldova.
Even after Estonia captain Ragnar Klavan was sent off for a second booking early in the second half in Tallinn, Hodgson's side still laboured to see off the Baltic minnows.
But they finally made the breakthrough thanks to Manchester United striker Rooney, who curled home a free-kick with 17 minutes remaining to maintain England's 100 percent record after three Group E matches.
Rooney is now within one goal of Jimmy Greaves and only six behind England record holder Bobby Charlton's tally of 49
Equally pleasing for Hodgson was seeing his rock-solid defence achieve a fifth successive clean sheet for the first time in eight years.
"It was hard work. We played well in the first half without taking our chances and that meant there was an air of frustration setting in," Hodgson told ITV.
"Everyone was aware that when you have played well you have to take at least one chance. Luckily we did that in the second half.
"It was a good free-kick from Wayne and it's four wins in a row, which is not to be sniffed at."
In Group G, Austria went top with seven points from three games after edging Montenegro 1-0 in Vienna thanks to a first-half goal from Rubin Okotie who converted a 24th-minute pass from Marko Arnutovic.
Montenegro star striker Mirko Vucinic saw two good chances well-saved by Robert Almer in the Austria goal.
Previous Group G leaders Russia were held to a second successive 1-1 draw and have five points from three games.
Russia, coached by Capello, drew 1-1 with Sweden on Thursday and 72 hours later, they were pegged back again when Moldova skipper Alexandru Epureanu scored in the 74th minute to cancel out Artem Dzyuba's opener from the penalty spot just a minute earlier.
Ukraine went joint top in Group C after Serhiy Sydorchuk struck on the stroke of half-time to earn a 1-0 win over Macedonia in Lviv.
It was Ukraine's second win in four days having also beaten Belarus by the same scoreline on Thursday.
Sunday's win could have been more impressive but Andriy Yarmolenko smashed a 47th-minute penalty against the crossbar.
Group leaders Slovakia, who stunned champions Spain on Thursday, travel to Belarus looking to preserve their 100 percent record while the Spaniards face little Luxembourg.